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Statistics
Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data.... that are not already on this list.
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In statistics, an ecological correlation is a correlation between two variables that are group means, in contrast to a correlation between two variables that describe individuals.... Ecological fallacy
Ecological fallacy
An ecological fallacy, often called an ecological inference fallacy, is an error in the interpretation of statistical data in an ecological study, whereby inferences about the nature of specific individuals are based solely upon aggregate statistics collected for the group to which those individuals belong.... Ecological study
Ecological study
An ecological study is an epidemiological study in which the unit of analysis is a population rather than an individual. For instance, an ecological study may look at the association between smoking and lung cancer deaths in different countries.... Econometrics
Econometrics
Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles.... Economic data
Economic data
Economic data are usually numerical time-series, i.e., sets of data for part or all of a single Economics or the international economy. When they are time-series the data sets are usually monthly but can be quarterly and annual.... Econometric model
Econometric model
Econometric models are statistical models used in econometrics. An econometric model specifies the statistics relationship that is believed to hold between the various economic quantities pertaining a particular economic phenomena under study.... Economic statistics
Economic statistics
Economic statistics is a branch of applied statistics focusing on the collection, processing, compilation and dissemination of statistics concerning the economy of a region, a country or a group of countries.... Eddy covariance
Eddy covariance
The eddy covariance technique is a prime atmospheric flux measurement technique to measure and calculate vertical turbulent fluxes within atmospheric boundary layers.... Edgeworth series
Edgeworth series
The Gram-Charlier A series and the Edgeworth series, named in honor of Francis Ysidro Edgeworth, are series_ that approximate a probability distribution in terms of its cumulants.... Effect size
Effect size
In statistics, effect size is a measure of the strength of the relationship between two variables. In scientific experiments, it is often useful to know not only whether an experiment has a statistical significance effect, but also the size of any observed effects.... Efficiency (statistics)
Efficiency (statistics)
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the desirability of an estimator or of an experimental design.... Eigenpoll
Eigenpoll
An eigenpoll is a type of statistical survey which gathers knowledge from the community. It differs from opinion polls by finding the best solution, rather than finding the most popular opinion.... Ellsberg paradox
Ellsberg paradox
The Ellsberg paradox is a paradox in decision theory and experimental economics in which people's choices violate the expected utility hypothesis.... Elston Stewart algorithm
Elston Stewart algorithm
The Elston-Stewart algorithm is an algorithm for computing the likelihood of observed genotype data given a pedigree. It is due to Robert Elston and John Stewart It can handle relatively large pedigrees providing they are outbred.... Empirical Bayes method
Empirical Bayes method
In statistics, empirical Bayes methods are a class of methods which use empirical data to evaluate/approximate the conditional probability distributions that arise from Bayes' theorem.... Empirical distribution function
Empirical distribution function
In statistics, an empirical distribution function is a cumulative distribution function that concentrates probability 1/n at each of the n numbers in a sample .... Empirical orthogonal functions
Empirical orthogonal functions
In statistics and signal processing, the method of empirical orthogonal function analysis is a decomposition of a signal processing or data set in terms of orthogonal basis functions which are determined from the data.... Empirical probability
Empirical probability
Empirical probability, also known as Frequency , or experimental probability, is the ratio of the number favorable outcomes to the total number of trials, not in a sample space but in an actual sequence of experiments.... Empirical process
Empirical process
The study of empirical processes is a branch of mathematical statistics and a sub-area of probability theory. It is a generalization of the central limit theorem for empirical measures.... Empirical statistical laws
Empirical statistical laws
An empirical statistical law or a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets.... Endogeneity (economics)
Endogeneity (economics)
In an economics model , parameters or variables are said to be endogenous when they are predicted by other variables in the model.For example, in a simple supply and demand model, when predicting the quantity demanded in equilibrium, the price is endogenous because producers change their price in response to demand and consumers change the... Energy statistics
Energy statistics
Energy statistics refers to collecting, compiling, analyzing and disseminating data on commodities such as coal, crude oil, natural gas, electricity, or renewable energy sources , when they are used for the energy they contain.... Encyclopedia of Statistical Sciences
Encyclopedia of Statistical Sciences
The Encyclopedia of Statistical Sciences is the largest-ever encyclopaedia of statistics. It is published by John Wiley & Sons.The first edition, in nine volumes, was edited by Norman Lloyd Johnson and Samuel Kotz and appeared in 1982.... (book)
Engineering statistics
Engineering statistics
Engineering statistics is a branch of statistics that has several subtopics which are particular to engineering:# or design of experiments uses statistical techniques to test and construct models of engineering components and systems.... Engset calculation
Engset calculation
The Engset calculation is a formula to determine the probability of congestion occurring within a telephony trunking. It was named after its developer, T.... Ensemble forecasting
Ensemble forecasting
Ensemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system.... Ensemble Kalman filter
Ensemble Kalman filter
The ensemble Kalman filter is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models....
Entropy (information theory)
Entropy estimation
Entropy estimation
Estimating the differential entropy of a system or process, given some observations, is useful in various science/engineering applications, such as Independent Component Analysis, , genetic analysis , speech recognition, manifold learning, and time delay estimation.... Entropy power inequality
Entropy power inequality
In mathematics, the entropy power inequality is a result in probability theory that relates to so-called "entropy power" of random variables. It shows that the entropy power of suitably well-behaved random variables is a superadditive function .... Epidata
Epidata
EpiData refers to a group of applications used in combination for creating documented data structures and analysis of quantitative data. The EpiData Association, which created the software, was created in 1999 and is based in Denmark.... – software
Epitome (image processing)
Epitome (image processing)
In , an epitome is a condensed digital representation of the essential statistical properties of ordered datasets, such as matrices representing s, audio signals, videos, or genetic sequences.... Epps effect
Epps effect
The Epps effect, named after T. W. Epps, is the phenomenon that the empirical cross correlation between the returns of two different stocks decreases as the sampling frequency of data increases.... Equiprobable
Equiprobable
Equiprobability is a philosophy concept in probability theory that allows one to assign equal probabilities to outcomes that are judged to be equipossible or to be "equally likely" .... Erlang distribution
Erlang distribution
The Erlang distribution is a continuous probability distribution with wide applicability primarily due to its relation to the exponential distribution and Gamma distribution distributions.... Ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systemswith an invariant measure and related problems. Its initial development was motivated by problems of statistical physics.... Error bar
Error bar
Error bars are used on graphs to indicate the Error#Experimental_science in a reported measurement. They give a general idea of how accurate a measurement is, or conversely, how far from the reported value the true value might be.... Errors and residuals in statistics
Errors and residuals in statistics
In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa... Errors-in-variables model
Errors-in-variables model
Total least squares, also known as errors in variables, rigorous least squares, or orthogonal regression, is a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account.... Estimating equations
Estimating equations
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimation. This can be thought of as a generalisation of the method of moments.... Estimation
Estimation
Estimation is the calculation approximation of a result which is usable even if input data may be incomplete or uncertainty.In statistics, see estimation theory, estimator.... Estimation theory
Estimation theory
Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data.... Estimation of covariance matrices
Estimation of covariance matrices
In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimation theory. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the Joint probability distribution....
Estimation of signal parameters via rotational invariance techniques
Estimator
Estimator
In statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population parameter ; an estimate is the result from the actual application of the function to a particular Sampling_ of data.... Etemadi's inequality
Etemadi's inequality
In probability theory, Etemadi's inequality is a so-called "maximal inequality", an inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound.... Event study
Event study
An Event study is a :statistics method to assess the impact of an event on the value of a firm. For example, the announcement of a merger between two :firms can be analyzed to see whether investors believe the merger will create or destroy value.... Evidence under Bayes theorem
Evidence under Bayes theorem
Among evidence scholars, the study of evidence in recent decades has become broadly interdisciplinary, incorporating insights from psychology, feminism, economics, and probability theory.... Evolutionary data mining
Evolutionary data mining
Evolutionary data mining, or genetic data mining is an umbrella term for any data mining using evolutionary algorithms. While it can be used for mining data from DNA sequences, it is not limited to biological contexts and can be used in any classification-based prediction scenario, which helps "predict the value ...... Ewens's sampling formula
Ewens's sampling formula
In population genetics, Ewens' sampling formula, introduced by Warren Ewens, states that under certain conditions , if a random sample of n gametes is taken from a population and classified according to the gene at a particular locus then the probability that there are a1 alleles represented once in the sample, and aExact statistics
Exact statistics
Exact statistics, such as that described in exact test, is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating procedures based on asymptotic analysis and approximate statistical methods.... Exact test
Exact test
In statistics, an exact test is a test where all assumptions upon which the derivation of the distribution of the test statistic is based are met, as opposed to an approximate test, in which the approximation may be made as close as desired by making the sample size big enough.... Examples of Markov chains
Examples of Markov chains
This page contains examples of Markov chains in action.... Excess risk
Excess risk
In statistics, excess risk is a measure of the association between a specified risk factor and a specified outcome . It is the difference between two proportions?in epidemiology it's typically defined to be the difference between the proportion of subjects in a population with a particular disease who were exposed to a specified risk factor a... Exchange paradox
Exchange paradox
The exchange paradox is a paradox within the probability theory and the decision theory which demonstrates problems that can arise when working with expected values....
Exchangeable random variables
Expander walk sampling
Expander walk sampling
The expander graph Random walk#Random walk on graphs Sampling theorem, the earliest version of which is due to Ajtai-Koml?s-Szemer?di and the more general version typically attributed to Gillman, states that sampling from an expander graph is almost as good as sampling statistical independence.... Expectation-maximization algorithm
Expectation-maximization algorithm
An expectation-maximizationalgorithm is used in statistics for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables.... Expected value
Expected value
In probability theory and statistics, the expected value of a random variable is the Lebesgue integral of the random variable with respect to its probability measure.... Expected value of sample information
Expected value of sample information
In decision theory, the expected value of sample information is the price that one would be willing to pay in order to gain access to a sample from the probability distribution about which the prediction has to be made.... Experiment
Experiment
In scientific inquiry, an experiment is a method of investigating causal relationships among variables. An experiment is a cornerstone of the empiricism approach to acquiring data about the world and is used in both natural sciences and social sciences.... Experimental design diagram
Experimental Design Diagram
Experimental Design Diagram is a diagram used by scientists, to Design of experiments an experiment. This diagram helps to identify the essential components of an experiment.... Experimental event rate
Experimental event rate
In epidemiology and biostatistics, the experimental event rate is a measure of how often a particular statistical event occurs within the experimental group of an experiment .... Experimental techniques
Experimental techniques
Experimental research designs are used for the controlled testing of causality processes. The general procedure is one or more independent variables are manipulated to determine their effect on a dependent variable.... Experimenter's bias
Experimenter's bias
In experimental science, experimenter's bias is bias towards a result expected by the human experimenter. David Sackett, in a useful review of biases in clinical studies, states that biases can occur in any one of seven stages of research:... Experimentwise error rate
Experimentwise error rate
In statistics, during multiple comparisons testing, experimentwise error rate is the probability of at least one false rejection of the null hypothesis over an entire experiment.... Explained sum of squares
Explained sum of squares
In statistics, an explained sum of squares is the sum of square d predicted values in a standard regression model , where is the response variable, is the explanatory variable, and are coefficients, indexes the observations from to , and is the error term.... Explained variation
Explained variation
In statistics, explained variation or explained randomness measures the proportion to which a mathematical model accounts for the variation of a given data set....
Explanatory variable
Exploratory data analysis
Exploratory data analysis
Exploratory data analysis is an approach to data analysis for the purpose of formulating hypothesis worth testing, complementing the tools of conventional statistics for testing hypotheses.... Exponential dispersion model
Exponential dispersion model
Exponential dispersion models are statistical models in which the probability distribution is of a special form. This class of models represents a generalisation of the exponential family of models which themselves play an important role in statistical theory because they have a special structure which enables deductions to be made about appr... Exponential distribution
Exponential distribution
In probability theory and statistics, the exponential distributions are a class of continuous probability distributions. They describe the times between events in a Poisson process, i.e.... Exponential family
Exponential family
In theory of probability and statistics, an exponential family is a class of probability distributions sharing a certain form, specified below. It is said that such distributions belong to the exponential class of density functions.... Exponential power distribution
Exponential power distribution
The exponential power distribution, also known as the generalized error distribution, is a probability distribution that takes a scale parameter a and exponent b....
Exponential random numbers &mash; redirect to subsection of Exponential distribution
Exponential distribution
In probability theory and statistics, the exponential distributions are a class of continuous probability distributions. They describe the times between events in a Poisson process, i.e.... Exponential smoothing
Exponential smoothing
In statistics, Exponential Smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts.... Exposure variable
Exposure variable
The exposure variable, in survival analysis, is the discrete or continuous variable which differentiates distinct failure events. It is usually time, especially the time to failure of a device, or the time to death of a person.... Extended Kalman filter
Extended Kalman filter
In estimation theory, the extended Kalman filter is the nonlinear version of the Kalman filter which linearizes about the current mean and covariance.... Extended negative binomial distribution
Extended negative binomial distribution
In probability and statistics the extended negative binomial distribution is a discrete probability distribution extending the negative binomial distribution.... External validity
External validity
External validity is the validity of generalized inferences in scientific studies, usually based on experiments as experimental Validity .Inferences about cause-effect relationships based on a specific scientific study are said to possess external validity if they may be generalized from the unique and idiosyncratic settings, procedures an... Extreme value theory
Extreme value theory
File:1755 Lisbon earthquake.jpgExtreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions....
lass="link1" onMouseover='showByLink("m875354",this)' onMouseout='hide("m875354")'href="http://www.absoluteastronomy.com/topics/Factorial_moment">Factorial moment
Factorial moment
In probability theory, the nth factorial moment of a probability distribution, also called the nth factorial moment of any random variable X with that probability distribution, is... Factorial moment generating function
Factorial moment generating function
In probability theory and statistics, the factorial moment generating function of the probability distribution of a real number random variable X is defined as... Failure rate
Failure rate
Failure rate is the frequency with which an engineered system or component failure, expressed for example in failures per hour. It is often denoted by the Greek alphabet ? and is important in reliability theory.... F-distribution
F-distribution
In probability theory and statistics, the F-distribution is a continuous probability distribution probability distribution. It is also known as Snedecor's F distribution or the Fisher-Snedecor distribution .... F-divergence
F-divergence
In probability theory, an f-divergence is a function If that measures the difference between two probability distributions P and Q.... F-test
F-test
An F-test is any statistical test in which the test statistic has an F-distribution if the null hypothesis is true. The name was coined by George W.... F1 score
F1 Score
In statistics, the F1 score is a measure of a test's accuracy. It considers both the Precision p and the Recall r of the test to compute the score: p is the number of correct results divided by the number of all returned results and r is the number of correct results divided by the number of results that should have been re... Factor analysis
Factor analysis
Factor analysis is a statistics method used to describe variance among observed variables in terms of fewer unobserved variables called factors.... Factorial code
Factorial code
Most real world data sets consist of data vectors whose individual components are not statistically independent, that is, they are redundant in the statistical sense.... Factorial experiment
Factorial experiment
In statistics, a factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.... Fair coin
Fair coin
In probability theory and statistics, a sequence of statistical independence Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.... Falconer's formula
Falconer's formula
Falconer's formula is used to determine the Genetics heritability of a trait based on the difference between twin correlations.The formula is hb2 = 2, where hb2 is the broad sense heritability, rmz is the identical twin correlation, and rdz is the fraternal twin correlation... False discovery rate
False discovery rate
False discovery rate control is a statistics method used in multiple testing to correct for multiple comparisons. In a list of rejected hypotheses, FDR controls the Expected value proportion of incorrectly rejected null hypothesis .... False negative
Type I and type II errors
In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr... False positive
Type I and type II errors
In statistics, the terms Type I error and type II error are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman and Egon Pearson , both eminent statisticians, discussed the problems associated with "deciding whether or not a particular sample may be judged as likely to have been randomly dr... False positive paradox
False positive paradox
The false positive paradox is a situation where the incidence of a condition is lower than the false positive rate of a test and therefore when the test shows that a condition exists, it is probable that the result is a false positive.... Familywise error rate
Familywise error rate
In statistics, familywise error rate is the probability of making one or more false discoveries, or Type I and type II errorss among all the hypotheses when performing multiple comparisons.... Fano factor
Fano factor
In probability theory and statistics, the Fano factor [Fano, 1947], like the coefficient of variation, is a measure of the statistical dispersion of a probability distribution.... Fast Fourier transform
Fast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex number to group theory and number theory; this article gives an overview of the available techniques and some of their general propert... Fast Kalman filter
Fast Kalman filter
The fast Kalman filter , devised by Antti Lange , is an extension of the Helmert-Wolf blocking method from geodesy to real-time applications of Kalman filtering such as satellite imaging of the Earth.... FastICA
FastICA
FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyv?rinen at Helsinki University of Technology.... – fast independent component analysis
Fat tail
Fat tail
A fat tail is a property of some probability distributions exhibiting extremely large kurtosis particularly relative to the ubiquitous normal distribution which itself is an example of an exceptionally thin tail distribution.... Feasible generalized least squares
Feasible generalized least squares
Feasible generalized least squares is a regression analysis technique. It is similar to generalized least squares except that it uses an estimated variance-covariance matrix since the true matrix is not known directly.... Feller process
Feller process
In mathematics, a Feller process is a particular kind of Markov process.... Feller-continuous process
Feller-continuous process
In mathematics, a Feller-continuous process is a continuous-time stochastic process satisfying a stronger continuous function property than simple sample continuous process.... Fiducial inference
Fiducial inference
Fiducial inference was a form of statistical inference put forward by Ronald Fisher in an attempt to perform inverse probability without prior probability distributions.... Field experiment
Field experiment
A field experiment applies the scientific method to experimentally examine an intervention in the real world rather than in the laboratory.... Fieller's theorem
Fieller's theorem
In statistics, Fieller's theorem allows the calculation of a confidence interval for the ratio of two arithmetic mean.Variables a and b may be measured in different units, so there is no way to directly combine the standard errors as they may also be in different units.... File drawer problem
File drawer problem
The file drawer problem is that many studies in a given area of research may be conducted but never reported, and those that are not reported may on average report different results from those that are reported.... Filtering problem (stochastic processes)
Filtering problem (stochastic processes)
In the theory of stochastic processes, the filtering problem is a mathematical model for a number of filtering problems in signal processing and the like.... Finite-dimensional distribution
Finite-dimensional distribution
In mathematics, finite-dimensional distributions are a tool in the study of Measure_theory and stochastic processes. A lot of information can be gained by studying the "projection" of a measure onto a finite-dimensional vector space .... First-hitting-time model
First-hitting-time model
In statistics, first-hitting-time models are a sub-class of survival analysis.... First-in-man study
First-in-man study
A first-in-man study is a clinical trial where a medical procedure, previously developed and assessed through in vitro or animal testing, or through mathematical modelling is tested on human subjects for the first time.... Fishburn–Shepp inequality
Fishburn–Shepp inequality
In combinatorics mathematics, the Fishburn?Shepp inequality is an inequality for the number of extensions of partial orders to linear orders, found by and .... Fisher consistency
Fisher consistency
Fisher consistency is a description of a statistical construct, used to describe probable outcomes within a certain set of "consistent outcomes".... Fisher information
Fisher information
In statistics and information theory, the Fisher information is the variance of the score . It is named in honor of its inventor, the statistician Ronald Fisher.... Fisher kernel
Fisher kernel
In mathematics, the Fisher kernel, named in honour of Sir Ronald Fisher, is a Integral transform. It was introduced in 1998 by Tommi Jaakkola.... Fisher transformation
Fisher transformation
In statistics, hypotheses about the value of the population correlation coefficient ρ between variables X and Y of the underlying population, can be tested using the Fisher transformation applied to the sample correlation r.... Fisher's exact test
Fisher's exact test
Fisher's exact test is a statistical significance test used in the analysis of contingency tables where sample sizes are small. It is named after its inventor, Ronald Fisher, and is one of a class of exact test, so called because the significance of the deviation from a null hypothesis can be calculated exactly rather than by relying on a t... Fisher's inequality
Fisher's inequality
In combinatorics mathematics, Fisher's inequality, named after Ronald Fisher, is a necessary condition for the existence of a balanced incomplete block design satisfying certain prescribed conditions....
Fisher's linear discriminator
Fisher's method
Fisher's Method
In statistics, Fisher's method, also known as Fisher's combined probability test, developed by and named for Ronald Fisher, is a data fusion or "meta-analysis" technique for combining the results from a variety of Statistical independence tests bearing upon the same overall hypothesis as if in a single large test.... Fisher's noncentral hypergeometric distribution
Fisher's noncentral hypergeometric distribution
In probability theory and statistics, Fisher's noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified by weight factors.... Fisher's z-distribution
Fisher's z-distribution
Fisher's z-distribution is the statistical distribution of half the logarithm of an F distribution variate:It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto, entitled "On a distribution yielding the error functions of several well-known statistics" ... Fisher-Tippett distribution
Fisher-Tippett distribution
In probability theory and statistics, the Gumbel distribution is used to model the distribution of the maximum of a number of samples of various distributions.... — redirects to Generalized extreme value distribution
Generalized extreme value distribution
In probability theory and statistics, the generalized extreme value distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel distribution, Frechet_distribution and Weibull distribution families also known as type I, II and III extreme value distributions.... Fisher–Tippet–Gnedenko theorem
Fisher–Tippet–Gnedenko theorem
In statistics, the Fisher?Tippet?Gnedenko theorem is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics.... Five-number summary
Five-number summary
File:Michelsonmorley-boxplot.svgIn descriptive statistics, the five-number summary of a data set consists of:# the sample minimum # the quartile or first quartile ... Fixed effects estimator
Fixed effects estimator
In econometrics and statistics the fixed effects estimator is an estimator for the coefficients in panel data analysis. If we assume fixed effects, we impose time independent effects for each entity.... — redirects to Fixed effects estimation
Fixed effects estimation
FLAME clustering
FLAME clustering
Fuzzy clustering by Local Approximation of MEmberships is a novel data clustering algorithm that defines clusters in the dense parts of a dataset and performs cluster assignment solely based on the neighborhood relationships among objects.... Fleiss' kappa
Fleiss' kappa
Fleiss' kappa is a statistical measure for assessing the inter-rater reliability between a fixed number of raters when assigning categorical ratings to a number of items or classifying items.... Fleming-Viot process
Fleming-Viot process
The term Fleming-Viot process refers to a particular subset of Markov_process as defined in the 1979 paper, "Some measure-valued Markov processes in population genetics theory", by Wendell H.... Floor effect
Floor effect
In statistics, the term floor effect refers to when data cannot take on a value lower than some particular number, called the floor.An example of this is when an IQ test is given to young children who have either been given training or have been given no training.... FNN algorithm
FNN algorithm
The false nearest neighbor algorithm is an algorithm for estimating the fractal dimension.... (false nearest neighbour algorithm)
Folded normal distribution
Folded Normal Distribution
The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean ? and variance s2, the random variable Y = |X| has a folded normal distribution.... Forecast error
Forecast error
In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest.... Forecasting
Forecasting
Forecasting is the process of estimation in unknown situations. Prediction is a similar, but more general term. Both can refer to estimation of time series, cross-sectional data or longitudinal study data.... Forest plot
Forest plot
A forest plot is a graphical display that shows the strength of the evidence in quantitative scientific studies. It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of randomized controlled trials.... Formation matrix
Formation matrix
In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the inverse of the observed information matrix of .... Foster's theorem
Foster's theorem
In probability theory, Foster's theorem, named after F. G. Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable state spaces.... Foundations of statistics
Foundations of statistics
Foundations of statistics is the usual name for the epistemology debate over how one should conduct inductive inference from data. Among issues considered are the question of Bayesian inference versus frequentist inference, the distinction between Ronald Fisher's "significance testing" and Jerzy Neyman-Egon Pearson "hypothesis testing", and... Founders of statistics
Founders of statistics
Statistics is the theory and application of mathematics to the scientific method including hypothesis generation, experimental design, Sampling , data collection, Summary statistics, Estimator, prediction and statistical inference from those results to the statistical population from which the experimental sample was drawn.... Fraction of variance unexplained
Fraction of variance unexplained
In statistics, the fraction of variance unexplained in the context of a Regression analysis is the amount of variance of the Regressand Y which cannot be explained, i.e., which is not correctly predicted, by the explanatory variable X.... Fractional Brownian motion
Fractional Brownian motion
A normalized fractional Brownian motion on is a continuous-time Gaussian process starting at zero, with mean zero, and having the following correlation function:...
Fractional factorial design
Fréchet distribution
Fréchet distribution
The Fr?chet distribution is a special case of the generalized extreme value distribution. It has the cumulative distribution functionwhere α>0 is a shape parameter.... Freedman-Diaconis rule
Freedman-Diaconis rule
In statistics, the Freedman-Diaconis rule can be used to select the size of the bins to be used in a histogram. The general equation for the rule is:... Freidlin-Wentzell theorem
Freidlin-Wentzell theorem
In mathematics, the Freidlin-Wentzell theorem is a result in the large deviations theory of stochastic processes. Roughly speaking, the Freidlin-Wentzell theorem gives an estimate for the probability that a sample path of an Ito diffusion will stray far from the mean path.... Frequency (statistics)
Frequency (statistics)
In statistics the frequency of an Event i is the number ni of times the event occurred in the experiment or the study. These frequencies are often graphically represented in histograms.... Frequency distribution
Frequency distribution
In statistics, a frequency statistical distribution is a tabulation of the values that one or more variables take in a Sampling .... Frequency probability
Frequency probability
Frequency probability is the Probability interpretations that defines an event's probability as the limit of its relative frequency in a large number of trials.... Friedman test
Friedman test
The Friedman test is a non-parametric statistics statistical test developed by the United States economist Milton Friedman. Similar to the parametric statistics repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts....
Fully-crossed design
Function approximation
Function approximation
The need for function approximations arises in many branches of applied mathematics, and computer science in particular. In general, a function approximation problem asks us to select a function among a well-defined class that closely matches a target function in a task-specific way.... Functional data analysis
Functional data analysis
Functional data analysis is a branch of statistics that analyzes data providing information about curves, surfaces or anything else varying over a continuum.... Funnel plot
Funnel plot
A funnel plot is a useful graph designed to check the existence of publication bias in meta-analysis.... Fuzzy logic
Fuzzy logic
Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. In binary sets with binary logic, in contrast to fuzzy logic named also crisp logic, the variables may have a Membership function of only 0 or 1.... Fuzzy measure theory
Fuzzy measure theory
Fuzzy measure theory considers a number of special classes of measures, each of which is characterized by a special property. Some of the measures used in this theory are plausibility and belief measures, fuzzy set Membership function and the classical probability measures.... FWL theorem
FWL theorem
In econometrics, the FWL theorem is named after the econometricians Ragnar Anton Kittil Frisch, F. Waugh, and M. Lovell.The Frisch-Waugh-Lovell Theorem states that if the regression we are concerned with is:... — relating regression and projection
In statistics, G-tests are likelihood ratio test or maximum likelihood statistical significance tests that are increasingly being used in situations where chi-square tests were previously recommended.... Galbraith plot
Galbraith plot
In statistics, a Galbraith plot , is one way of displaying several estimates of the same quantity that have different standard errors. It can be used to examine heterogeneity#statistics in a meta-analysis, as an alternative or supplement to a forest plot.... Gallagher Index
Gallagher Index
The Gallagher Index is used to measure the disproportionality of an electoral outcome, that is the difference between the percentage of votes received and the percentage of seats a party gets in the resulting legislature....
Galton–Watson process
Galton's problem
Galton's problem
Galton?s problem, named after Sir Francis Galton, is the problem of drawing inferences from Cross-cultural studies data, due to the statistical phenomenon now called autocorrelation.... Gambler's fallacy
Gambler's fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated statistical independence trials of some random process then these deviations are likely to be evened out by opposite deviations in the future.... Gambler's ruin
Gambler's ruin
The term gambler's ruin is used for a number of related statistical ideas. The original meaning is that a gambling who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet.... Gamma distribution
Gamma distribution
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. It has a scale parameter θ and a shape parameter k.... Gamma test (statistics)
Gamma test (statistics)
A gamma test tests the strength of Association of the cross tabulation data when both variables are measured at the ordinal level. It makes no adjustment for either table size or ties.... Gamma process
Gamma process
A Gamma process is a L?vy process with Statistical independence Gamma distribution increments. Often written as , it is a pure-jump increasing Levy process with intensity measure , for positive ....
Gamma variate
Gauss–Kuzmin distribution
Gauss–Markov process
Gauss–Markov process
Gauss?Markov stochastic processes are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes.Every Gauss-Markov process X possesses the three following properties:... Gauss–Markov theorem
Gauss–Markov theorem
In statistics, the Gauss?Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear model in which the errors have expectation zero and are uncorrelated and have equal variances, a best linear bias of an estimator estimator of the coefficients is given by the least-squares estimator.... Gaussian function
Gaussian function
In mathematics, a Gaussian function is a function of the form:for some real number constants a > 0, b, c > 0, and e ? 2.718281828 .... Gaussian measure
Gaussian measure
In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics.... Gaussian process
Gaussian process
In the mathematical theory of probability, a Gaussian process is a stochastic process t ?T for which any finite linear combination of sampling will be normal distribution .... Geary's C
Geary's C
Geary's C is a measure of spatial autocorrelation. Like autocorrelation, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated.... GEH
GEH
The GEH Statistic is a formula used in traffic engineering, traffic forecasting, and traffic modelling to compare two sets of traffic volumes. The GEH formula gets its name from Geoffrey E.... — a statistic comparing modelled and observed counts
General linear model
General linear model
The general linear model is a statistical linear model.It may be written aswhere Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors and residuals in statistics.... General matrix notation of a VAR(p)
General matrix notation of a VAR(p)
Vector_AutoregressionThis page just shows the details for different matrix notations of a Vector autoregression process with k variables.... Generalizability theory
Generalizability theory
Generalizability theory is a statistical framework for conceptualizing, investigating, and designing reliable observations. It was originally introduced by Lee Cronbach and his colleagues.... Generalized additive model
Generalized additive model
In statistics, the generalized additive model is a statistical model developed by Trevor Hastie and Rob Tibshirani for blending properties of generalized linear models with additive models.... Generalized canonical correlation
Generalized canonical correlation
In statistics, the generalized canonical correlation analysis , is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets.... Generalized Dirichlet distribution
Generalized Dirichlet distribution
In statistics, the generalized Dirichlet distribution is a generalization of the Dirichlet distribution with a more general covariance structure and twice the number of parameters.... Generalized estimating equations
Generalized estimating equations
Generalized estimating equations are used in statistics to goodness-of-fit the parameters of a Generalized linear model where unknown correlation is present.... Generalized extreme value distribution
Generalized extreme value distribution
In probability theory and statistics, the generalized extreme value distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel distribution, Frechet_distribution and Weibull distribution families also known as type I, II and III extreme value distributions....
Generalized Gaussian distribution
Generalised hyperbolic distribution
Generalised hyperbolic distribution
The generalised hyperbolic distribution is a continuous probability distribution defined as the normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian distribution.... Generalized inverse Gaussian distribution
Generalized inverse Gaussian distribution
In probability theory and statistics, the generalized inverse Gaussian distribution is a three-parameter family of continuous probability distributions with probability density function... Generalized linear array model
Generalized linear array model
In statistics, the generalized linear array model is used for analyzing the data sets with array structure. It based on the generalized linear model with the regression matrix written as a Kronecker product.... Generalized linear mixed model
Generalized linear mixed model
In statistics, a generalized linear mixed model is a particular type of mixed model . It is an extension to the generalized linear model in which the linear predictor contains random effects in addition to the usual fixed effects.... Generalized linear model
Generalized linear model
In statistics, the generalized linear model is a flexible generalization of ordinary linear regression. It relates the random distribution of the measured variable of the experiment to the systematic portion of the experiment through a function called the link function.... Generalized method of moments
Generalized method of moments
The generalized method of moments is a very general statistics method for obtaining point estimation of parameters of statistical models. It is a generalization, developed by Lars Peter Hansen, of the method of moments ....
Generalized multidimensional scaling
Generalized normal distribution
Generalized normal distribution
The generalized normal distribution or generalized Gaussian distribution can refer to either of two families of parametric statistics continuous probability distributions on the real number line.... Generalized Procrustes analysis
Generalized Procrustes analysis
The origin of generalized Procrustes analysis has a strong basis in the comparison of research results across languages . It was developed to permit statistical analysis of the results of free-choice profiling which allows respondents to develop their own terms for attributes that describe a range of products in their own wods or language .... Generative model
Generative model
In statistics, a generative model is a model for randomly generating observable data, typically given some hidden parameters. It specifies a joint distribution over observation and label sequences.... GenStat
GenStat
GenStat is a general statistical package. Early versions were developed for large Mainframe computer computers. Up until version 5, there was a Unix binary available, and this continues to be used by many universities and research institutions.... – software
Geodemographic segmentation
Geodemographic Segmentation
Geodemographic segmentation is a Multivariate statistics classification technique for discovering whether the individuals of a population fall into different groups by making quantitative comparisons of multiple characteristics with the assumption that the differences within any group should be less than the differences between groups.... Geometric Brownian motion
Geometric Brownian motion
A geometric Brownian motion is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion, or a Wiener process.... Geometric data analysis
Geometric data analysis
Geometric data analysis can refer to geometry aspects of , pattern analysis and shape analysis or the approach of multivariate statistics that treats arbitrary data sets as clouds of points in n-dimensional space.... Geometric distribution
Geometric distribution
In probability theory and statistics, the geometric distribution is either of two discrete probability distributions:* the probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set , or... Geometric median
Geometric median
The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions.... Geometric standard deviation
Geometric standard deviation
In probability theory and statistics, the geometric standard deviation describes how spread out are a set of numbers whose preferred average is the geometric mean.... Geostatistics
Geostatistics
Geostatistics is a branch of geology that deals with the analysis of mining processes through mathematical models. Evolved originally in the exploration of minerals, ores, and coals, it is currently applied in disciplines such as petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geography, forestry, environm... German tank problem
German tank problem
File:PantherTankColor.jpgIn the statistical theory of estimation theory, estimating the maximum of a uniform distribution is a common illustration of differences between estimation methods.... Gerschenkron effect
Gerschenkron effect
The Gerschenkron effect was developed by Alexander Gerschenkron, and claims that changing the base year for an index determines the growth rate of the index.... Gibbs sampling
Gibbs sampling
In mathematics and physics, Gibbs sampling is an algorithm to generate a sequence of samples from the joint probability of two or more random variables.... Gini coefficient
Gini coefficient
The Gini coefficient is a Statistical_dispersion#Measures_of_statistical_dispersion most prominently used as a income inequality metrics or Wealth condensation.... Gittins index
Gittins index
In machine learning theory, the Gittins index is commonly related to the classic multi-armed bandit problem. A two-armed bandit is a slot machine with two levers, each with a different probability of payoff.... GLIM (software)
GLIM (software)
GLIM is a statistical software program for fitting generalized linear models .It was developed by the Royal Statistical Society Working Party on Statistical Computing... &ndash software
Glivenko-Cantelli theorem
Glivenko-Cantelli theorem
In the theory of probability, the Glivenko?Cantelli theorem determines the asymptotic behaviour of the empirical distribution function as the number of iid observations grows....
Gompertz function
Gompertz-Makeham law of mortality
Gompertz-Makeham law of mortality
The Gompertz-Makeham law states that death rate is a sum of age-independent component and age-dependent component , which increases exponentially with age.... Good-Turing frequency estimation
Good-Turing frequency estimation
Good?Turing frequency estimation is a statistical technique for predicting the probability of occurrence of objects belonging to an unknown number of species, given past observations of such objects and their species.... Goodhart's law
Goodhart's law
Although Goodhart's law has been expressed in a variety of formulations, the essence of the law is that once a social or economic indicator or other surrogate measure is made a target for the purpose of conducting social or economic policy, then it will lose the information content that would qualify it to play such a role.... Goodman and Kruskal's lambda
Goodman and Kruskal's lambda
In probability theory and statistics, Goodman & Kruskal's lambda is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a level of measurement#Nominal_measurement independent variable and dependent variable , it indicates the extent to which the modal categories and frequencies for each value of the... Goodness of fit
Goodness of fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question....
Gordon–Newell network
Gordon–Newell theorem
Gordon–Newell theorem
In queueing theory, a discipline within the mathematical probability theory, the Gordon?Newell theorem is an extension of Jackson's theorem from open queueing networks to closed queueing networks of exponential servers.... Graeco-Latin square
Graeco-Latin square
In mathematics, a Graeco-Latin square or Euler square of order n over two Set s S and T, each consisting of n symbols, is an n×n arrangement of cells, each cell containing an ordered pair , where s ∈ S and a t ∈ T, such that... Grand mean
Grand mean
The grand mean is the mean of the means of several subsamples. For example, consider several lots, each containing several items. The items from each lot are sampling for a measure of some variable and the means of the measurements from each lot are computed.... Granger causality
Granger causality
Granger causality is a technique for determining whether one time series is useful in forecasting another. Ordinarily, regressions reflect "mere" correlations, but Clive Granger, who won a Nobel Prize in Economics, argued that there is an interpretation of a set of tests as revealing something about causality.... Graph cuts in computer vision
Graph cuts in computer vision
As applied in the field of computer vision, Cut can be employed to Polynomial time solve a wide variety of low-level computer vision problems , such as image smoothing, the stereo correspondence problem, and many other computer vision problems that can be formulated in terms of energy minimization.... – a potential application of Bayesian analysis
Graphical model
Graphical model
In probability theory, statistics, and machine learning, a graphical model is a graph that represents statistical independence among random variables.... Gravity model of trade
Gravity model of trade
The gravity model of trade in international economics, similar to other gravity models in social science, predicts bilateral trade flows based on the economic sizes of and distance between two units.... Gretl
Gretl
gretl is an open-source statistical package, mainly for econometrics. The name is an acronym for GNU General Public License Regression, Econometrics and Time-series Library.... Group method of data handling
Group method of data handling
Group method of data handling is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully-automatic structural and parametric optimization of models.... Group size measures
Group size measures
Many animals, including humans, tend to live in groups, herds, flock , bands, Pack , parties, or Bird colony of conspecific individuals. The size of these groups, as expressed by the number of participant individuals, is an important aspect of their social environment.... Grubbs' test for outliers
Grubbs' test for outliers
Many statistical techniques are sensitive to the presence of outliers. For example, simple calculations of the mean and standard deviation may be distorted by a single grossly inaccurate data point.... Guess value
Guess value
A guess value is more commonly called a starting value or initial value. These are necessary for most optimization problems which use search algorithms, because those algorithms are mainly Deterministic algorithm and iterative, and they need to start somewhere.... Guesstimate
Guesstimate
Guesstimate is a portmanteau of the words guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture....
Gumbel distribution
Guttman scale
Guttman scale
In statistical surveys conducted by means of structured interviews or questionnaires, a subset of the survey items having binary answers forms a Guttman scale if they can be ranked in some order so that, for a rational respondent, the response pattern can be captured by a single index on that ordered scale.... Gy's sampling theory
Gy's sampling theory
Gy's sampling theory is a scientific theory about the sampling of materials, developed by Pierre Gy in articles and books including:* Sampling nomogram...
The Hadamard variance is a measure of stability of clocks and oscillators. It uses 3-sample variance, not unlike the Allan variance, which uses 2-sample variance.... Half circle distribution
Half circle distribution
In probability theory and statistics, the half-circle distribution is a continuous probability distribution defined by the unique half-circle that goes between [-r , r], where r = radius, whose area is one.... Half-logistic distribution
Half-logistic distribution
In probability theory and statistics, the half-logistic distribution is a continuous probability distribution—the distribution of the absolute value of a random variable following the logistic distribution.... Half-normal distribution
Half-normal distribution
The half-normal distribution is the probability distribution of the absolute value of a random variable that is normal distribution with expected value 0 and variance s2.... Halton sequences
Halton sequences
In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are Deterministic system they are of Low-discrepancy sequence, that is, appear to be random for many purposes.... Hamburger moment problem
Hamburger moment problem
In mathematics, the Hamburger moment problem, named after Hans Hamburger, is formulated as follows: given a sequence , does there exist a positive Borel measure ? on the real line such that... Hannan-Quinn information criterion
Hannan-Quinn information criterion
Information criteria are often used as a guide in model selection . The Kullback-Leibler quantity of information contained in a model is the distance from the... Harris chain
Harris chain
In the mathematical study of stochastic processes, a Harris chain is a Markov chain satisfying an additional property.... Hartley's test
Hartley's test
In statistics, Hartley's test, also known as the Fmax test or Hartley's Fmax, is used in the analysis of variance to verify that different groups have a similar variance, an assumption needed for other statistical tests.... Hat matrix
Hat matrix
In statistics, the hat matrix, H, relates the fitted values to the observed values. It describes the influence each observed value has on each fitted value.... Hausdorff moment problem
Hausdorff moment problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moment ... Hausman specification test
Hausman specification test
The Hausman specification test is the first easy method allowing scientists to evaluate if their statistical models correspond to the data.It was developed by Jerry A. Hausman.... Hausman test
Hausman test
The Hausman test is a statistics test in econometrics named after Jerry Hausman. The test evaluates the significance of an estimator versus an alternative estimator.... note merger proposal with Hausman specification test
Hausman specification test
The Hausman specification test is the first easy method allowing scientists to evaluate if their statistical models correspond to the data.It was developed by Jerry A. Hausman....
Hazard function — redirects to Failure rate
Failure rate
Failure rate is the frequency with which an engineered system or component failure, expressed for example in failures per hour. It is often denoted by the Greek alphabet ? and is important in reliability theory.... Hazard ratio
Hazard ratio
The hazard ratio in survival analysis is the effect of an explanatory variable on the hazard or risk of an event. For a less technical definition than is provided here, consider hazard ratio to be an estimate of relative risk and see the explanation on that page.... Heaps' law
Heaps' law
In linguistics, Heaps' law is an empirical law which describes the portion of a vocabulary which is represented by an instance document consisting of words chosen from the vocabulary.... Heart rate variability
Heart rate variability
Heart rate variability is a measure of the beat-to-beat variations in heart rate. It is usually calculated by analyzing a time series of beat-to-beat intervals from the ECG, of beat-to-beat intervals derived from an arterial pressure tracing or of beat-to-beat intervals derived from a pulse wave signal measured by means of a photoplethysmogr... Heavy-tailed distribution
Heavy-tailed distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.... Heckman correction
Heckman correction
The Heckman correction is any of a number of related statistical methods developed by James Heckman in 1976 through 1979 which allow the researcher to correct for selection bias.... Hedonic regression
Hedonic regression
In economics, hedonic regression, also hedonic demand theory, is a method of estimating demand or value . It decomposes the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic.... Hellinger distance
Hellinger distance
In probability theory, a branch of mathematics, given two probability measures P and Q that are absolute continuity in respect to a third probability measure λ, the square of the Hellinger distance between P and Q is defined as the quantity... Helmert-Wolf blocking
Helmert-Wolf blocking
The Helmert-Wolf blocking is a least squares solution for a sparse system of linear equations. Friedrich Robert Helmert reported on the use of such systems for geodesy in his book "Die mathematischen und physikalischen Theorieen der h?heren Geod?sie, 1.... Herfindahl index
Herfindahl index
The Herfindahl index, also known as Herfindahl-Hirschman Index or HHI, is a measure of the size of corporations in relation to the industry and an indicator of the amount of competition among them....
Heteroscedasticity
Heteroscedasticity-consistent standard errors
Heteroscedasticity-consistent standard errors
In statistics, a frequent assumption in linear regression is that the disturbances ui have the same variance. When this is not the case, we get heteroskedasticity in the estimated residuals .... Hidden Markov model
Hidden Markov model
A hidden Markov model is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters; the challenge is to determine the hidden parameters from the observable data.... Hidden semi-Markov model
Hidden semi-Markov model
A hidden semi-Markov model is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov process rather than Markov process .... Hierarchical Bayes model
Hierarchical Bayes model
The hierarchical Bayes method is one of the most important topics in modern Bayesian analysis. It is a powerful tool for expressing rich statistical models that more fully reflect a given problem than a simpler model could.... Hierarchical hidden Markov model
Hierarchical hidden Markov model
The Hierarchical hidden Markov model is a statistical model derived from the hidden Markov model . In an HHMM each state is considered to be a self contained probabilistic model.... Hierarchical linear modeling
Hierarchical linear modeling
In statistics, hierarchical linear modeling , also known as multilevel model, is a more advanced form of simple linear regression and multiple linear regression.... High-dimensional statistics
High-dimensional statistics
High-dimensional statistics is a branch of mathematical and applied multivariate statistics aimed at the treatment of statisical data whose dimension is so large that it is comparable in magnitude to the sample size and may be much greater.... Higher-order factor analysis
Higher-order factor analysis
Higher-order factor analysis is a statistical method consisting of repeating steps factor analysis ? oblique rotation ? factor analysis of rotated factors...... Higher-order statistics
Higher-order statistics
Higher-order statistics measures are extensions of second-order measures to higher orders.... Histogram
Histogram
In statistics, a histogram is a graphical display of tabulated frequency , shown as bars. It shows what proportion of cases fall into each of several Categorization.... Historiometry
Historiometry
Historiometry is the History study of human progress or individual personal characteristics, using statistics to analyze references to famous people, their statements, behavior and discoveries in relatively neutral texts.... History of statistics
History of statistics
Statistics arose, no later than the 18th century, from the need of states to collect data on their people and economies, in order to administer them. Its meaning broadened in the early 19th century to include the collection and analysis of data in general.... Hodges-Lehmann estimator
Hodges-Lehmann estimator
The Hodges-Lehmann estimator is a statistical method for Robust statistics.The principal form of this estimator is used to give an estimate of the difference between the values in two sets of data.... Holm-Bonferroni method
Holm-Bonferroni method
In statistics, the Holm-Bonferroni method performs more than one Statistical hypothesis testing simultaneously. It is named after Sture Holm and Carlo Emilio Bonferroni.... Homogeneity (statistics)
Homogeneity (statistics)
In statistics, homogeneity arises in describing the properties of a dataset, or several datasets, and relates to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part.... Homoscedasticity
Homoscedasticity
In statistics, a sequence or a vector of random variables is homoskedastic if all random variables in the sequence or vector have the same finite set variance....
Hoover index
Hotelling's T-square distribution
Hotelling's T-square distribution
In statistics, Hotelling's T-square statistic, named for Harold Hotelling,is a generalization of Student's t distribution that is used in multivariate hypothesis testing.... How to Lie with Statistics
How to Lie with Statistics
How to Lie with Statistics is a book written by Darrell Huff in 1954 presenting an introduction to statistics for the general reader. It is a brief, breezy, illustrated volume outlining common errors, both intentional and unintentional, associated with the interpretation of statistics, and how these errors can lead to inaccurate conclus... (book)
Howland will forgery trial
Howland will forgery trial
The Howland will forgery trial was a United States court case in 1868 to decide Henrietta Howland Robinson's contest of the Will of Sylvia Ann Howland.... Huber-White standard errors
Huber-White standard errors
In econometrics, Huber-White standard errors are standard errors that are adjusted for correlations of error terms across observations, especially in panel and survey data as well as data with cluster structure.... Hubbert curve
Hubbert curve
The Hubbert curve projects the rate of oil production over time, and is the main component of Hubbert peak theory. It was first proposed by geophysicist M....
Human subject research
Hurst exponent
Hurst exponent
In fractal geometry, the generalized Hurst exponent, named H_%28disambiguation%29 in honor of both Harold Edwin Hurst and Otto_Ludwig_Holder by Beno%C3%AEt_Mandelbrot, is referred to as the "index of dependence," and is the relative tendency of a time series to either strongly regress to the mean or 'cluster' in a direction.... Hyper-exponential distribution
Hyper-exponential distribution
In probability theory, a hyper-exponential distribution is a continuous distribution such that the probability density function of the random variable is given by... Hyper-Graeco-Latin square design
Hyper-Graeco-Latin square design
In the design of experiments, hyper-Graeco-Latin squares are efficient designs to study the effect of one primary factor in the presence of 4 blocking factors.... Hyperbolic distribution
Hyperbolic distribution
The hyperbolic distribution is a continuous probability distribution that is characterized by the fact that the logarithm of the probability density function is a hyperbola.... Hyperbolic secant distribution
Hyperbolic secant distribution
In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and Characteristic function are proportional to the hyperbolic function.... Hypergeometric distribution
Hypergeometric distribution
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement, just as the binomial distribution describes the number of successes for draws with replacement.... Hyperparameter
Hyperparameter
In Bayesian statistics, a hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model for the underlying system under analysis.... Hyperprior
Hyperprior
In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, a parameter of a prior distribution.As with the term hyperparameter, the use of hyper is to distinguish it from a prior distribution of a parameter of the model for the underlying system.... Hypoexponential distribution
Hypoexponential distribution
In probability theory the hypoexponential distribution or the generalized Erlang distribution is a continuous distribution, that has found use in the same fields as the Erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes....
lass="link1" onMouseover='showByLink("m875571",this)' onMouseout='hide("m875571")'href="http://www.absoluteastronomy.com/topics/Idealised_population">Idealised population
Idealised population
main article: effective population sizeIn population genetics an idealised population, also sometimes called a Fisher-Wright population after Ronald Fisher and Sewall Wright, is a population whose members can Sexual intercourse and reproduce with any other member of the other gender, has a sex ratio of 1 and no overlapping generat... Ignorability
Ignorability
In statistics, ignorability refers to an experiment design where the method of data collection do not have a significant influence on the intrepretation of the data.... Illustration of the central limit theorem
Illustration of the central limit theorem
This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.... Image denoising
Image denoising
Image denoising often refers to the recovery of an image from its noisy version contaminated by additive white Gaussian noise . Although other types of noise have also been studied in the literature of image processing, the term of ?image denoising? is usually devoted to the problem associated with AWGN.... Importance sampling
Importance sampling
In statistics, importance sampling is a general technique for estimating the properties of a particular probability distribution, while only having samples generated from a different distribution rather than the distribution of interest.... Imprecise probability
Imprecise probability
The notion of Imprecise probability is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities.... Imputation (statistics)
Imputation (statistics)
In statistics, imputation is the substitution of some value for a missing data point or a missing component of a data point. Once all missing values have been imputed, the dataset can then be analysed using standard techniques for complete data.... Inclusion probability
Inclusion probability
In the theory of finite population sampling , the inclusion probability of an element is its probability of becoming part of the sample during the drawing of a single sample.... Increasing process
Increasing process
An increasing process is a stochastic processwhere the random variables which make up the process are increasing almost surely and adapted process:... Indecomposable distribution
Indecomposable distribution
In probability theory, an indecomposable distribution is any probability distribution that cannot be represented as the distribution of the sum of two or more non-constant statistical independence random variables.... Independent component analysis
Independent component analysis
Independent component analysis is a computational method for separating a multivariate signal into additive subcomponents supposing the mutual statistical independence of the non-Gaussian source signals.... Independent and identically-distributed random variables
Independent and identically-distributed random variables
In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed if each has the same probability distribution as the others and all are mutually statistical independence....
Index of dispersion
Index number
Index number
An index number is an economic data figure reflecting price or quantity compared with a standard or base value. The base usually equals 100 and the index number is usually expressed as 100 times the ratio to the base value.... Indicators of spatial association
Indicators of spatial association
Indicators of spatial association are statistics that evaluate the existence of Cluster analysis in the space arrangement of a given variable. For instance if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance a... Indirect least squares
Indirect least squares
Indirect least squares is an approach in econometrics where the coefficients in a system of equations are estimated from the reduced form model using ordinary least squares.... Inductive inference
Inductive inference
Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols.... An inequality on location and scale parameters
An inequality on location and scale parameters
For probability distributions having an expected value and a median, the mean and the median can never differ from each other by more than one standard deviation.... Inference
Inference
Inference is the act or process of deriving a logical consequence from premises.Inference is studied within several different fields.* Human inference is traditionally studied within the field of cognitive psychology....
Inferential statistics redirects to Statistical inference
Statistical inference
Inferential statistics or statistical induction comprises the use of statistics to make inferences concerning some unknown aspect of a population.... Infinite divisibility (probability)
Infinite divisibility (probability)
The concepts of infinite divisibility and the Decomposable distributions arise in probability and statistics in relation to seeking families of probability distributions that might be a natural choice in certain applications, in the same way that the normal distribution is.... Information bottleneck method
Information bottleneck method
The information bottleneck method is a technique introduced by Tishby et al [1] for finding the best tradeoff between accuracy and complexity when random variable a random variable X, given a joint probability distribution between X and an observed relevant variable Y.... Information geometry
Information geometry
In mathematics and especially in statistical inference, information geometry is the study of probability and information theory by way of differential geometry.... Information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E.... Inherent bias
Inherent bias
The term "inherent bias" refers to the effect of underlying factors or assumptions that skew viewpoints a subject under discussion. There are multiple formal definitions of "inherent bias" which depend on the particular field of study.... Inherent zero
Inherent zero
In statistics, an inherent zero is a reference point used to describe data sets which are indicative of magnitude of an absolute or relative nature. Inherent zeros are used on ratio scales.... Injury prevention
Injury prevention
Injury prevention are efforts to prevent or reduce the severity of bodily injury caused by external mechanisms, such as accidents, before they occur.... – application
Instrumental variable
Instrumental variable
In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables is used to estimate causal relationships when controlled experiments are not feasible.... Intention to treat analysis
Intention to treat analysis
In epidemiology, an intention to treat analysis is an analysis based on the initial treatment intent, not on the treatment eventually administered.... Interaction (statistics)
Interaction (statistics)
In statistics, an interaction is a term in a statistical model added when the effect of two or more variables is not simply additive function. Such a term reflects that the effect of one variable depends on the values of one or more other variables.... Interaction variable
Interaction variable
In statistics, an interaction variable is a variable often used in regression analysis. It is formed by the multiplication of two independent variables.... Interclass correlation
Interclass correlation
In statistics, the interclass correlation measures a bivariate relation among variables.The Pearson correlation coefficient is the most commonly used interclass correlation.... Interclass dependence
Interclass dependence
In statistics, interclass dependence means that the occurrence of one class is statistical independence on other classes that may occur in the same space.... Interim analysis
Interim analysis
Clinical trials are unique in that enrolment of patients is a continual process staggered in time. This means that if a treatment is particularly beneficial or harmful compared to the concurrent placebo group while the study is on-going, the investigators are ethically obliged to assess that difference using the data at hand and to make a deliberat... Internal consistency
Internal consistency
In statistics and research, internal consistency is a measure based on the correlations between different items on the same test . It measures whether several items that propose to measure the same general construct produce similar scores.... Internal validity
Internal validity
Internal validity is the validity of inferences in scientific studies, usually based on experiments as experimental Validity .Details ... Interquartile mean
Interquartile mean
The 'interquartile mean ' is a statistics measures of central tendency, much like the mean , the median, and the mode .The IQM is a truncated mean and so is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining score... Interquartile range
Interquartile range
In descriptive statistics, the interquartile range , also called the midspread, middle fifty and middle of the #s, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles.... Inter-rater reliability
Inter-rater reliability
Inter-rater reliability, inter-rater agreement, or concordance is the degree of agreement among raters. It gives a score of how much :wikt:homogeneity, or consensus, there is in the ratings given by judges.... Interval estimation
Interval estimation
In statistics, interval estimation is the use of Sampling data to calculate an interval of possible values of an unknown population parameter, in contrast to point estimation, which is a single number.... Intervening variable
Intervening variable
An intervening variable is a hypothetical internal state that is used to explain relationships between observed variables, such as independent and dependent variables, in empirical research.... Intraclass correlation
Intraclass correlation
In statistics, the intraclass correlation is a measure of correlation, consistency or conformity for a data set when it has multiple groups.The intra-class correlation is used to estimate the correlation of one variable between two members within a group, for instance between two children of one family.... Invariant estimator
Invariant estimator
In statistics, an invariant estimator is a criterion that can be used to compare the properties of different estimators, formalising the idea that an estimator should have certain intuitively appealing qualities.... Inverse-chi-square distribution
Inverse-chi-square distribution
In probability and statistics, the inverse-chi-square distribution is the probability distribution of a random variable whose multiplicative inverse has a chi-square distribution.... Inverse-gamma distribution
Inverse-gamma distribution
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the multiplicative inverse of a variable distributed according to the gamma distribution.... Inverse Gaussian distribution
Inverse Gaussian distribution
In probability theory, the inverse Gaussian distribution is a two-parameter family of continuous probability distributions with support on .... Inverse distance weighting
Inverse distance weighting
Inverse distance weighting is a method for multivariate interpolation, a process of assigning values to unknown points by using values from usually scattered set of known points.... Inverse Mills ratio
Inverse Mills ratio
In statistics, the inverse Mills ratio, named after John P. Mills, is the ratio of the probability density function over the cumulative distribution function of a distribution.... Inverse-Wishart distribution
Inverse-Wishart distribution
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability density function defined on matrix ....
Inverse transform sampling
Iris flower data set
Iris flower data set
The Iris flower data set or Fisher's Iris data set is a multivariate data set introduced by Ronald Fisher as an example of discriminant analysis.... Irwin-Hall distribution
Irwin-Hall distribution
In probability theory and statistics, the Irwin-Hall distribution is a continuous probability distribution of the sum of n i.i.d. Uniform distribution random variables:... Isomap
Isomap
In statistics, Isomap is one of several widely used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling .... Isotonic regression
Isotonic regression
In numerical analysis, isotonic regression involves finding a weighted least-squares fit to a Euclidean space with weights vector subject to a set of monotonicity constraints giving a totally ordered set or partial order over the variables.... Item response theory
Item response theory
In psychometrics, item response theory is a body of theory describing the application of mathematical models to data from questionnaires and Test as a basis for measurement abilities, attitudes, or other variables.... Item tree analysis
Item tree analysis
Item tree analysis is a Data analysis method which allows constructing ahierarchical structure on the items of a questionnaire or test from observed response... Iteratively re-weighted least squares
Iteratively re-weighted least squares
The method of iteratively re-weighted least squares is a numerical analysis for minimizing any specified objective function using a standard weighted least squares method such as Gaussian elimination.... Ito's lemma
Ito's lemma
In mathematics, Kiyoshi Ito's Lemma is used in Ito calculus to find the differential of a function of a particular type of stochastic process....
In statistics, resampling is any of a variety of methods for doing one of the following:# Estimating the precision of sample statistics by using subsets of available data or drawing randomly with replacement from a set of data points ...
Jackson network
Jackson's theorem (queueing theory)
Jadad scale
Jadad scale
The Jadad scale, sometimes known as Jadad scoring or the Oxford quality scoring system, is a procedure to independently assess the methodological quality of a clinical trial.... James-Stein estimator
James-Stein estimator
The James-Stein estimator is a nonlinear estimator which can be shown to dominating decision rule, or outperform, the "ordinary" technique. As such, it is the best-known example of Stein's phenomenon....
Jarque–Bera test
Jeffreys prior
Jeffreys prior
In Bayesian probability, the Jeffreys prior, named after Harold Jeffreys, is a non-informative prior prior distribution on parameter space that is proportional to the square root of the Fisher information:... Jensen–Shannon divergence
Jensen–Shannon divergence
In probability theory and statistics, the Jensen-Shannon divergence is a popular method of measuring the similarity between two probability distributions.... JMulTi
JMulTi
JMulTi is an open-source interactive software for econometric analysis, specialised in univariate and multivariate time series analysis. It has a Java graphical user interface.... – software
Joint probability distribution
Jump process
Jump process
A jump process is a type of stochastic process that has large discrete movements , rather than small continuous movements.This concept is frequently used in finance....
Jump-diffusion model
The -means algorithm is an algorithm to data clustering objects based on attributes into partition of a set, . It is similar to the expectation-maximization algorithm for mixtures of Gaussian distribution in that they both attempt to find the centers of natural clusters in the data.... K-medoids
K-medoids
The -medoids algorithm is a data clustering algorithm related to the k-means algorithm and the medoidshift algorithm. Both the -means and -medoids algorithms are partitional and both attempt to minimize mean square error, the distance between points labeled to be in a cluster and a point designated as the center of that cluster.... Kalman filter
Kalman filter
The Kalman filter is an efficient recursive filter that estimates the state of a Linear system from a series of noise measurements. It is used in a wide range of engineering applications from radar to computer vision, and is an important topic in control theory and control systems engineering.... Kaplan-Meier estimator
Kaplan-Meier estimator
The Kaplan-Meier estimator estimates the survival function from life-time data. In medical research, it might be used to measure the fraction of patients living for a certain amount of time after treatment....
Kappa coefficient
Kappa statistic
Karhunen-Ločve theorem
Karhunen-Ločve theorem
In the theory of stochastic processes, the Karhunen-Lo?ve theorem is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval.... Kendall tau distance
Kendall tau distance
The Kendall tau distance is a Metrics that counts the number of pairwise disagreements between two lists. The larger the distance, the more dissimilar the two lists are.... Kendall tau rank correlation coefficient
Kendall tau rank correlation coefficient
The Kendall tau rank correlation coefficient is a non-parametric statistic used to measure the degree of correspondence between two rankings and assessing the significance of this correspondence.... Kendall's W
Kendall's W
Kendall's W is a non-parametric statistic. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters.... – Kendall's coefficient of concordance
Kent distribution
Kent distribution
The 5-parameter Fisher-Bingham distribution or Kent distribution, named after Ronald Fisher, Christopher Bingham, and John T. Kent, is a probability distribution on the two-dimensional unit sphere in .... Kernel density estimation
Kernel density estimation
In statistics, kernel density estimation is a Non-parametric statistics way of Density estimation the probability density function of a random variable.... Kernel methods
Kernel methods
Kernel Methods are a class of algorithms for pattern analysis, whose best known elementis the Support Vector Machine . The general task of pattern analysis is to find and study general types of relations in general types of data .... Kernel regression
Kernel regression
The kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y.... Kernel smoother
Kernel smoother
A kernel smoother is a statistics technique for estimating a real valued function by using its noisy observations, when non-parametric statistics for this function is known.... Kernel (statistics)
Kernel (statistics)
A kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable.... Khmaladze transformation
Khmaladze transformation
Consider the sequence of empirical distribution functions based on asequence of i.i.d random variables, , as n increases.Suppose is the hypothetical distribution function of... (probability theory)
Killed process
Killed process
In mathematics — specifically, in stochastic processes — a killed process is a stochastic process that is forced to assume an undefined or "killed" state at some time.... Kirkwood approximation
Kirkwood approximation
The Kirkwood superposition approximation was introduced by Matsuda as a means of representing a discrete probability distribution. The name apparently refers to a 1942 paper by John G.... Kitchen sink regression
Kitchen sink regression
A kitchen sink regression is an informal and usually pejorative term for a regression analysis which uses a long list of possible independent variables to attempt to explain variance in a dependent variable.... Kolmogorov backward equation
Kolmogorov backward equation
The Kolmogorov backward equation and its Adjoint of an operator the Kolmogorov forward equation are partial differential equations that arise in the theory of continuous-time continuous-state Markov processes.... Kolmogorov continuity theorem
Kolmogorov continuity theorem
In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constrains on the moment of its increments will be continuous .... Kolmogorov’s criterion
Kolmogorov’s criterion
In probability theory, Kolmogorov's criterion, named after Andrey Kolmogorov, is a theorem in Markov processes which states that a stationary Markov chain with transition matrix P and state space S is time reversibility if and only if its transition probabilities satisfy... Kolmogorov’s generalized criterion
Kolmogorov’s generalized criterion
Andrey Kolmogorov generalized criterion is a proposition in Markov process which states that a stationary Markov process with state space and generator matrix has reversed process with generator matrix if and only if... Kolmogorov's inequality
Kolmogorov's inequality
In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound....
Kolmogorov–Smirnov test
Kriging
Kriging
Kriging is a group of geostatistics techniques to interpolation the value of a random field at an unobserved location from observations of its value at nearby locations.... Kruskal-Wallis one-way analysis of variance
Kruskal-Wallis one-way analysis of variance
In statistics, the Kruskal-Wallis one-way analysis of variance by ranks is a non-parametric statistics for testing equality of population medians among groups.... Kuder-Richardson Formula 20
Kuder-Richardson Formula 20
In statistics, the Kuder-Richardson Formula 20 first published in 1937 is a measure of internal consistency Reliability for measures with dichotomous choices.... Kuiper's test
Kuiper's test
Kuiper's test is a statistics' test named after dutch statistician Nicolaas Kuiper that compares two distributions.Kuiper's test is closely related to the more well-known Kolmogorov-Smirnov test .... Kullback–Leibler divergence
Kullback–Leibler divergence
In probability theory and information theory, the Kullback?Leibler divergence is a non-commutative measure of the difference between two probability distributions P and Q.... Kumaraswamy distribution
Kumaraswamy distribution
In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval [0,1] differing in the values of their two non-negative shape parameters, a and b.... Kurtosis
Kurtosis
In probability theory and statistics, kurtosis is a measure of the "peakedness" of the probability distribution of a real number-valued random variable....
In robust statistics, an L-estimator is an estimator which equals a linear combination of order statistics of the measurements.Consider, for example, the median.... Lack-of-fit sum of squares
Lack-of-fit sum of squares
In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well.... Lag operator
Lag operator
In time series analysis, the lag operator or backshift operator operates on an element of a time series to produce the previous element. For example, given some time series... Landau distribution
Landau distribution
In probability theory, the Landau distribution is a probability distribution named after Lev Landau. It is defined by the complex number integral... Lander–Green algorithm
Lander–Green algorithm
The Lander?Green algorithm is an algorithm, due to Eric Lander and Philip Green for computing the likelihood of observed genotype data given a pedigree.... Laplace distribution
Laplace distribution
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also known as the double exponential distribution, because it can be thought of as two exponential distributions spliced together back-to-back.... Laplace principle (large deviations theory)
Laplace principle (large deviations theory)
In mathematics, Laplace's principle is a basic theorem in large deviations theory, similar to Varadhan's lemma. It gives an Asymptotic analysis for the Lebesgue integration of exp over a fixed set A as θ becomes large.... Large deviations of Gaussian random functions
Large deviations of Gaussian random functions
A random function – of either one variable , or two or more variables – is called Gaussian if every finite-dimensional distribution is a multivariate normal distribution....
LARS — see least-angle regression
Least-angle regression
In statistics, least-angle regression is a regression algorithm for high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.... Latent variable
Latent variable
In statistics, latent variables , are variables that are not directly observed but are rather inferred from other variables that are observed and directly measured.... , latent variable model
Latent variable model
A latent variable model is a statistical model that relates a set of variables to set of latent variables.It is assumed that 1) the responses on the indicators or manifest variables are the result of... Latent class model
Latent class model
In statistics, a latent class model relates a set of observed discrete multivariate variables to a set of latent variables. It is a type of latent variable model.... Latent Dirichlet allocation
Latent Dirichlet allocation
In statistics, latent Dirichlet allocation is a generative model that allows sets of observations to be explained by Latent variable groups which explain why some parts of the data are similar.... Latent growth modeling
Latent growth modeling
Latent growth modeling is a statistical technique used in the structural equation modeling framework to estimate growth trajectory. It is a longitudinal analysis technique to estimate growth over a period of time.... Latent semantic analysis
Latent semantic analysis
Latent semantic analysis is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms.... Latin square
Latin square
A Latin square is an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.... Latin hypercube sampling
Latin hypercube sampling
The statistics method of Latin hypercube sampling was developed to generate a distribution of plausible collections of parameter values from a multidimensional distribution.... Law (stochastic processes)
Law (stochastic processes)
In mathematics, the law of a stochastic process is the Measure that the process induces on the collection of Function from the index set into the state space.... Law of averages
Law of averages
The law of averages is a Layman's terms used to express a belief that outcomes of a random event shall "even out" within a small sample.As invoked in everyday life, the "law" usually reflects bad statistics or wishful thinking rather than any mathematical principle.... Law of large numbers
Law of large numbers
The law of large numbers is a theorem in probability that describes the long-term stability of the arithmetic mean of a random variable. Given a random variable with a finite expected value, if its values are repeatedly sampled, as the number of these observations increases, their mean will tend to approach and stay close to the expected va... Law of the iterated logarithm
Law of the iterated logarithm
In probability theory,the law of the iterated logarithm is the name given to several theorems which describe the magnitude of the fluctuations of a random walk.... Law of total cumulance
Law of total cumulance
In probability theory and mathematics statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance.... Law of total expectation
Law of total expectation
The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, the smoothing theorem, among other names, states that if X is an integrable random variable and Y is any random variable, not necessarily integrable, on the same probability space, then... Law of total probability
Law of total probability
In probability theory, the law of total probability is that "the prior probability of A is equal to the prior expected value of the posterior probability of A." That is, for any random variable N,... Law of total variance
Law of total variance
In probability theory, the law of total variance or variance decomposition formula states that if X and Y are random variables on the same probability space, and the variance of X is finite, then... Law of Truly Large Numbers
Law of Truly Large Numbers
The Law of Truly Large Numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen.... Layered hidden Markov model
Layered hidden Markov model
The layered hidden Markov model is a statistical model derived from the hidden Markov model .A layered hidden Markov model consists of N levels of HMMs, where the HMMs on level i + 1 correspond to observation symbols or probability generators at level i.... Least absolute deviations
Least absolute deviations
Least absolute deviations , also known as Least Absolute Errors , Least Absolute Value , or the L1 norm problem, is a mathematics optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data.... Least-angle regression
Least-angle regression
In statistics, least-angle regression is a regression algorithm for high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.... Least squares
Least squares
The method of least squares or ordinary least squares is used to solve overdetermined systems. Least squares is often applied in statistical contexts, particularly regression analysis.... Least-squares estimation of linear regression coefficients
Least-squares estimation of linear regression coefficients
In parametric statistics, the least-squares estimator is often used to estimate the coefficients of a linear regression. The least-squares estimator optimizes a certain criterion .... Least-squares spectral analysis
Least-squares spectral analysis
Least-squares spectral analysis is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis....
Learning theory (statistics)
Lee–Yang theorem
Lee–Yang theorem
In statistical mechanics, the Lee-Yang theorem states that if Partition function of certain models in statistical field theory with ferromagnetic interactions are considered as functions of an external field, then all zeros... Leftover hash-lemma
Leftover hash-lemma
Imagine that you have a secret key that has uniform random bits, and you would like to use this secret key to encrypt a message. Unfortunately, you were a bit careless with the key, and know that an adversary was able to learn about bits of that key, but you do not know which.... Lehmann–Scheffé theorem
Lehmann–Scheffé theorem
In statistics, the Lehmann?Scheff? theorem, named after Erich Leo Lehmann and Henry Scheff?, states that any unbiased estimator based only on a completeness , sufficiency statistic is the unique best unbiased estimator of its expected value.... Length time bias
Length time bias
Length time bias is a form of selection bias, a statistical distortion of results which can lead to incorrect conclusions about the data. Length time bias can occur when the lengths of intervals are analysed by selecting intervals that occupy randomly chosen points in time or space.... Levene's test
Levene's test
In statistics, Levene's test is an inferential statistic used to assess the equality of variance in different samples. Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal.... Level of measurement
Level of measurement
The "levels of measurement" is an expression which typically refers to the theory of scale types developed by the Harvard psychologist Stanley Smith Stevens.... Leverage (statistics)
Leverage (statistics)
In statistics, leverage is a term used in connection with regression analysis and, in particular, in analyses aimed at identifying those observations which have a large effect on the outcome of fitting regression models....
Levey-Jennings chart
Lévy continuity theorem
Lévy continuity theorem
The L?vy continuity theorem in probability theory, named after the French mathematician Paul Pierre L?vy, is the basis for one approach to prove the central limit theorem and it is one of the central theorems concerning Characteristic function s.... Lévy distribution
Lévy distribution
In probability theory and statistics, the L?vy distribution, named after Paul Pierre L?vy, is a continuous probability distribution for a non-negative random variable.... Lévy process
Lévy process
In probability theory, a L?vy process, named after the French mathematician Paul Pierre L?vy, is any continuous-time stochastic process that starts at 0, admits c?dl?g modification and has "stationary independent increments" ? this phrase will be explained below.... Lexis ratio
Lexis ratio
The Lexis ratio is used in statistics as a measure which seeks to evaluate differences between the statistical properties of random mechanisms where the outcome is two-valued — for example "success" or "failure", "win" or "lose".... Lies, damned lies, and statistics
Lies, damned lies, and statistics
"Lies, damned lies, and statistics" is part of a phrase attributed to Benjamin Disraeli and popularised in the United States by Mark Twain: "There are three kinds of lies: lies, damned lies, and statistics." The statement refers to the persuasive power of numbers, the use of statistics to bolster weak arguments, and the tendency of people to... Life expectancy
Life expectancy
Life expectancy is the average number of years of life remaining at a given age. It is the average expected lifespan of an individual. Life expectancy is heavily dependent on the criteria used to select the group.... Life table
Life table
In actuarial science, a life table is a table which shows, for a person at each age, what the probability is that they die before their next birthday.... Lift (data mining)
Lift (data mining)
In data mining, lift is a measure of the performance of a model at segmenting the population. The lift of a subset of the population is defined as the predicted response rate for that subset divided by the predicted response rate for the population.... Likelihood function
Likelihood function
In statistics, the likelihood function is a function of the parameters of a statistical model that plays a key role in statistical inference. In non-technical usage, "likelihood" is a synonym for "probability", but throughout this article only the technical definition is used.... Likelihood principle
Likelihood principle
In statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a Sampling is contained in the likelihood function.... Likelihood-ratio test
Likelihood-ratio test
The likelihood ratio, often denoted by , is the ratio of the maximum probability of a result under two different hypotheses. A likelihood-ratio test is a statistical test for making a decision between two hypotheses based on the value of this ratio.... Lilliefors test
Lilliefors test
In statistics, the Lilliefors test, named after Hubert Lilliefors, professor of statistics at George Washington University, is an adaptation of the Kolmogorov?Smirnov test.... Limiting density of discrete points
Limiting density of discrete points
The limiting density of discrete points is used to formulate an adjustment made by Edwin Thompson Jaynes to Claude Elwood Shannon's fundamental uniqueness theorem.... Lindeberg's condition
Lindeberg's condition
In probability theory, Lindeberg's condition is a Necessary and sufficient condition for the central limit theorem to hold for a sequence of independent random variables.... Lindley's paradox
Lindley's paradox
Lindley's paradox describes a counterintuitive situation in statistics in which the Bayesian inference and frequentist approaches to a hypothesis testing problem give opposite results for certain choices of the prior distribution.... Line chart
Line chart
A line chart or line graph is a type of graph of a function created by connecting a series of data points together with a line.... Line-intercept sampling
Line-intercept sampling
In statistics, line-intercept sampling is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a ?transect?, intersects the element .... Linear classifier
Linear classifier
In the field of machine learning, the goal of classification is to group items that have similar Features values, into groups. A linear classifier achieves this by making a classification decision based on the value of the linear combination of the features.... Linear discriminant analysis
Linear discriminant analysis
Linear discriminant analysis and the related Fisher's linear discriminant are methods used in statistics and machine learning to find the linear combination of Features s which best separate two or more classes of objects or events.... Linear model
Linear model
Disambiguation : go here for the Linear model of innovationIn statistics, given a sample the most general form of linear model is formulated as... Linear prediction
Linear prediction
Linear prediction is a mathematical operation where future values of a discrete time Signal processing are estimated as a linear transformation of previous samples....
Linear probability model
Linear regression
Linear regression
In statistics, linear regression is used for two things;Linear regression is a form of regression analysis in which the relationship between one or more independent variables and another variable, called the dependent variable, is modeled by a least squares function, called linear regression equation.... LISREL
LISREL
LISREL, an acronym for linear structural relations, is a statistical software package used in structural equation modeling. LISREL was developed in 1970s by Karl_J?reskog and Dag S?rbom, both professors of Uppsala University, Sweden.... — proprietary statistical software package
List of basic statistics topics
List of basic statistics topics
Statistics is a Mathematics pertaining to the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and Misuse of statistics for making informed decisions in all areas of business and government.... List of convolutions of probability distributions
List of convolutions of probability distributions
In probability theory, the probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions.... List of graphical methods
List of graphical methods
This is a list of graphical methods with a mathematical basis.Included are diagram techniques, chart techniques, Plot techniques, and other forms of visualization.... List of information graphics software
List of information graphics software
This is a list of software to create any kind of information graphics:* either includes the ability to create one or more infographics from a provided data set... List of probability topics
List of probability topics
This is a list of probability topics, by Wikipedia page.It overlaps with the list of statistical topics. There are also the Catalog of articles in probability theory, list of probabilists and list of statisticians.... List of random number generators
List of random number generators
Computer random number generators are important in mathematics, cryptography and gambling. This list includes all common types, regardless of quality.... List of scientific journals in statistics
A statistical package is a suite of computer programs that are specialised for statistics. It enables people to obtain the results of standard statistical procedures and statistical significance tests, without requiring low-level numerical programming.... List of statisticians
List of statisticians
Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning.... Listwise deletion
Listwise deletion
In statistics, listwise deletion is a method used to exclude any data with missing values from statistical analysis. For example, suppose a questionnaire has 20 items.... Ljung-Box test
Ljung-Box test
The Ljung-Box test is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test....
Local convex hull
Local independence
Local independence
Local independence is the underlying assumption of latent variable models.The observed items are independent of each other given an individual score on the latent variable.... Local regression
Local regression
LOESS, or locally weighted scatterplot smoothing, is one of many "modern" statistical model that build on classical statistics, such as linear and nonlinear Regression analysis....
Location estimation redirects to Location parameter
Location parameter
In statistics, a location family is a class of probability distributions parametrized by a scalar- or vector-valued parameter ?, which determines the "location" or shift of the distribution.... Location estimation in sensor networks
Location estimation in sensor networks
Location estimation in wireless sensor networks is the problem of Estimation theory the location of an object from a set of noisy measurements, when the measurements are acquired in a distributed... Location parameter
Location parameter
In statistics, a location family is a class of probability distributions parametrized by a scalar- or vector-valued parameter ?, which determines the "location" or shift of the distribution.... Location-scale family
Location-scale family
In probability theory, especially as that field is used in statistics, a location-scale family is a family of univariate probability distributions parametrized by a location parameter μ and a scale parameter σ ≥ 0; if X is any random variable whose probability distribution belongs to such a family, then Y =&... Locality (statistics)
Locality (statistics)
In statistics, locality is central tendency of a data set. More frequently, the word location is used. Thus the mean and median are measures of locality.... Log-Laplace distribution
Log-Laplace distribution
In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution.... Log-normal distribution
Log-normal distribution
In probability and statistics, the log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normal distribution....
Log-linear model
Log-linear modeling
Log-linear modeling
In economics, a model economy can be approximated with a log-linear system of equations. The log-linearized system is often easier to solve and easier to estimate with statistics.... Log-logistic distribution
Log-logistic distribution
In probability and statistics, the log-logistic distribution is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, for example mortality from cancer following diagnosis or treatment.... Logarithmic distribution
Logarithmic distribution
In probability and statistics, the logarithmic distribution is a discrete probability distribution derived from the Maclaurin series expansion... Logistic distribution
Logistic distribution
In probability theory and statistics, the logistic distribution is a continuous probability distribution.Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks.... Logistic function
Logistic function
A logistic function or logistic curve is the most common sigmoid curve. It modelsthe S-curve of growth of some set P, where P might... Logistic regression
Logistic regression
In statistics, logistic regression is a model used for prediction of the probability of occurrence of an event by fitting data to a logistic curve.... Logit
Logit
The logit function is the inverse of the "sigmoid", or logistic function used in mathematics, especially in statistics. The logit of a number p between 0 and 1 is given by the formula:... Logit analysis in marketing
Logit analysis in marketing
Logit analysis is a statistical technique used by marketing to assess the scope of customer acceptance of a product , particularly a new product.... Lognormal distribution
Log-normal distribution
In probability and statistics, the log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normal distribution.... Logrank test
Logrank test
In statistics, the logrank test is a hypothesis test to compare the survival analysis distributions of two samples. It is a nonparametric test and appropriate to use when the data are right censored .... Long-range dependency
Long-range dependency
Long-range dependency is a phenomenon that may arise in time series analysis and which may also arise in the analysis of spatial data. It relates to the rate of decay of statistical dependence, with the implication that this decays more slowly than an exponential decay, typically a power-like decay.... Long-tail traffic
Long-tail traffic
This article covers a range of tools from different disciplines that may be used in the important science of determining the probability of rare events....
Longitudinal regression
Longitudinal study
Longitudinal study
A longitudinal study is a correlational research study that involves repeated observations of the same items over long periods of time — often many decades.... Lorenz curve
Lorenz curve
In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of a probability distribution; it is a graph of a function showing the proportion of the distribution assumed by the bottom y% of the values.... Loss function
Loss function
In statistics, decision theory and economics, a loss function is a function that maps an event onto a real number representing the economic cost or regret associated with the event.... Lotka's law
Lotka's law
Lotka's law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law. It describes the frequency of publication by authors in any given field.... Low birth weight paradox
Low birth weight paradox
The low birth weight paradox is an apparently paradoxical observation relating to the birth weights and mortality of children born to tobacco smoking mothers.... Lucia de Berk
Lucia de Berk
Lucia de Berk is a Dutch nurse who was sentenced to life imprisonment in 2003 for four murders and three attempted murders of patients in her care.... – prob/stats related court case
Lumpability
Lumpability
In probability theory, lumpability is a method for reducing the size of the state space of some continuous-time Markov chains first published by Kemeny and Snell.... Lusser's law
Lusser's Law
Lusser's law is a prediction of reliability named after Robert Lusser. It states that the reliability of a series system is equal to the product of the reliability of its component subsystems, if their failure modes are known to be statistically independent.... Lyapunov's central limit theorem
Lyapunov's central limit theorem
In probability theory, Lyapunov's condition or Liapunov's condition or Lyapunov's central limit theorem is one of the variants of the central limit theorem....
lass="link1" onMouseover='showByLink("m875786",this)' onMouseout='hide("m875786")'href="http://www.absoluteastronomy.com/topics/M_slash_M_slash_1_model">M/M/1 model
M/M/1 model
The M/M/1 is a single-server queueing model, that can be used to approximate a lot of simple systems.Following Kendall's notation it indicates a system where:... M-estimator
M-estimator
In statistics, M-estimators are a broad class of statistics which are obtained as the solution to the problem of minimizing certain functions of the data....
*Redescending M-estimator
Redescending M-estimator
Redescending M-estimators are very popular ?-type M-estimators which have ? functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin.... M-separation
M-separation
In statistics, m-separation is a measure of disconnectedness in ancestral graphs and a generalization of d-separation for directed acyclic graphs.... Machine learning
Machine learning
Machine learning is the subfield of artificial intelligence that is concerned with the design and development of algorithms that allow computers to improve their performance over time based on data, such as from sensor data or databases.... Mahalanobis distance
Mahalanobis distance
In statistics, Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in 1936. It is based on correlations between variables by which different patterns can be identified and analyzed.... Main effect
Main effect
In the design of experiments and analysis of variance, a main effect is the effect of an independent variable on a dependent variable averaging across the levels of any other independent variables.... Mallows' Cp
Mallows' Cp
In statistics, Mallows' Cp, named after Colin Mallows, is often used as a stopping rule for various forms of stepwise regression. This was not Mallows' intention - he proposed the statistic only as a way of facilitating comparisons among many alternative subset regressions, and warned against its use as a decision rule.... MANCOVA
MANCOVA
Multivariate analysis of covariance is an extension of analysis of covariance methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined....
Mann–Whitney U
MANOVA
MANOVA
Multivariate analysis of variance is a generalized form of analysis of variance methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined.... Mantel test
Mantel test
The Mantel test is a statistics test of the correlation between two matrix . The matrices must be of the same rank of a matrix, in most applications they are matrices of interrelations between the same vector spaces of objects....
MAP estimator
Margin of error
Margin of error
The margin of error is a statistic expressing the amount of random sampling error in a statistical survey's results. The larger the margin of error, the less faith one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole Statistical population.... Marginal distribution
Marginal distribution
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.... Marginal likelihood
Marginal likelihood
In Bayesian probability probability theory, a marginal likelihood function is a likelihood function integrated over some variables, typically model parameters.... Marginal model
Marginal model
In statistics, marginal models are a technique for obtaining regression estimates in multilevel modeling, also called hierarchical linear models....
Marginal variable — redirects to Marginal distribution
Marginal distribution
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.... Mark and recapture
Mark and recapture
Mark and recapture is a method commonly used in ecology to estimate population size. This method is most valuable when a researcher fails to detect all individuals present within a population of interest every time that researcher visits the study area.... Markov blanket
Markov blanket
In machine learning, the Markov blanket for a Vertex in a Bayesian network is the set of nodes composed of 's parents, its children, and its children's other parents.... Markov chain
Markov chain
In mathematics, a Markov chain, named after Andrey Markov, is a stochastic process with the Markov property. Having the Markov property means that, given the present state, future states are independent of the past states. In other words, the description of the present state fully captures all the information that could influence th...
*Markov chain geostatistics
Markov chain geostatistics
Markov chain geostatistics refer to the Markov chain models, simulation algorithms and associated spatial correlation measures based on the Markov_network theory, which extends a single Markov chain into a multi-dimensional field for geostatistical modeling....
*Markov chain mixing time
Markov chain mixing time
In mathematical probability, a fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution π and, regardless of the initial state, the time-t distribution of the chain converges to π as t tends to infinity.... Markov chain Monte Carlo
Markov chain Monte Carlo
Markov chain Monte Carlo method methods , are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its Markov chain#Steady-state_analysis_and_limiting_distributions.... Markov decision process
Markov decision process
Markov decision processes , named after Andrey Markov, provide a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of the decision maker.... Markov information source
Markov information source
In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.... Markov logic network
Markov logic network
A Markov logic network is a probabilistic logic which applies the ideas of a Markov network to first-order logic. Markov logic networks generalize first-order logic, in the sense that, in a certain limit, all unsatisfiable statements have a probability of zero, and all entailment formula have probability one.... Markov network
Markov network
A Markov network, or Markov random field, is a model of the joint probability distribution of a set of random variables having the Markov property.... Markov process
Markov process
A Markov process, named after the Russian mathematician Andrey Markov, is a mathematical model for the random evolution of a memoryless system, that is, one for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states.... Markov property
Markov property
In mathematics, the term Markov property or Markov-type property can refer to either of two closely-related things.In the narrowest sense, a stochastic process has the Markov property if the conditional probability distribution of future states of the process, given the present state and a constant number of past states, depends... Marsaglia polar method
Marsaglia polar method
In computer science – in particular, in applications of the Monte Carlo method – the Marsaglia polar method is a method for generating a pair of... Martingale (probability theory)
Martingale (probability theory)
In probability theory, a martingale is a stochastic process such that the conditional expected value of an observation at some time t, given all the observations up to some earlier time s, is equal to the observation at that earlier time s.... Martingale representation theorem
Martingale representation theorem
In probability theory, the martingale representation theorem states that a random variable which is measurable with respect to the Filtration #Measure theory generated by a Brownian motion can be written in terms of an It? integral with respect to this Brownian motion.... Matching pursuit
Matching pursuit
File:Matching pursuit.pngMatching pursuit is a type of numerical technique which involves finding the "best matching" projections of multidimensional data onto an over-complete dictionary .... Mathematical biology
Mathematical biology
Mathematical biology/Theoretical biology includes at least four major subfields: Biological mathematical modeling, Relational biology/Complex systems biology , Bioinformatics and Computational biomodeling/biocomputing, and is an interdisciplinary research field of academic study with a wide range of applications in Bio... Mathematical modelling in epidemiology
Mathematical modelling in epidemiology
It is possible to mathematically model the progress of most infectious diseases to discover the likely outcome of an epidemic or to help manage them by vaccination.... Mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a purely mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis.... Matrix normal distribution
Matrix normal distribution
The matrix normal distribution is a probability distribution that is a generalization of the normal distribution to matrix-valued random variables.... Matrix population models
Matrix population models
Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix population models are a specific type of population model that uses matrix algebra.... Mauchly's sphericity test
Mauchly's sphericity test
Mauchly's sphericity test is a Statistics used to validate repeated measures factor ANOVAs. The test was introduced by ENIAC co-inventor John Mauchly in 1940.... Maximal ergodic theorem
Maximal ergodic theorem
The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics.Suppose that is a probability space, that is a measure-preserving transformation, and that .... Maximum a posteriori
Maximum a posteriori
In statistics, the method of maximum a posteriori estimation theory can be used to obtain a point estimation of an unobserved quantity on the basis of empirical data....
Maximum entropy classifier redirects to Logistic regression
Logistic regression
In statistics, logistic regression is a model used for prediction of the probability of occurrence of an event by fitting data to a logistic curve....
Maximum entropy method redirects to Principle of maximum entropy
Principle of maximum entropy
The principle of maximum entropy is a postulate about a universal feature of any probability assignment on a given set of propositions . Let some testable information about a probability distribution function be given.... Maximum entropy probability distribution
Maximum entropy probability distribution
In statistics and information theory, a maximum entropy probability distribution is a probability distribution whose information entropy is at least as great as that of all other members of a specified class of distributions.... Maximum entropy spectral estimation
Maximum entropy spectral estimation
The maximum entropy method applied to spectral density estimation. The overall idea is that the maximum entropy rate stochastic process that satisfies the given constant autocorrelation and variance constraints, is a linear Gauss-Markov_process with i.i.d.... Maximum likelihood
Maximum likelihood
Maximum likelihood estimation is a popular statistics method used for fitting a mathematical model to data. The modeling of real world data using estimation by maximum likelihood offers a way of tuning the free parameters of the model to provide a good fit.... Maximum parsimony
Maximum parsimony
Parsimony is a non-parametric statistics method commonly used in computational phylogenetics for estimating phylogeny. Under parsimony, the preferred phylogenetic tree is the tree that requires the least evolutionary change to explain some observed data.... Maximum spacing estimation
Maximum spacing estimation
In mathematics, Maximum spacing estimation , or maximum product of spacing estimation , is a statistics method for fitting the parameters of a mathematical model to data .... Maxwell speed distribution
Maxwell Speed Distribution
In the classical picture of an ideal gas, molecules bounce around at a variety of different velocities, never interacting with each other. Though this qualitative picture is obviously flawed , it is a useful model for situations where the particle density is very low; in a more quantitative sense, this means that the particles themselves are very... Maxwell–Boltzmann distribution
Maxwell–Boltzmann distribution
The Maxwell?Boltzmann distribution is a probability distribution with applications in physics and chemistry. The most common application is in the field of statistical mechanics.... MCAR
MCAR
In Statistics, data that are missing completely at random in a data set when the event that a particular item is missing is statistical independence of observable variables and unobservable parameters of interest.... (missing completely at random)
McCullagh's parametrization of the Cauchy distributions
McCullagh's parametrization of the Cauchy distributions
In probability theory, the "standard" Cauchy distribution is the probability distribution whose probability density function isfor x real number.... McDiarmid's inequality
McDiarmid's inequality
McDiarmid's inequality, named after Colin McDiarmid, is a result in probability theory that gives an upper bound on theprobability for the value of a function depending on multiple independent random variables to deviate from its expected value.... McNemar's test
McNemar's test
In statistics, McNemar's test is a non-parametric method used on nominal data to determine whether the row and column marginal frequencies are equal.... Mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
Mean – see also expected value
Expected value
In probability theory and statistics, the expected value of a random variable is the Lebesgue integral of the random variable with respect to its probability measure.... Mean absolute error
Mean absolute error
In statistics, the mean absolute error is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by... Mean absolute percentage error
Mean Absolute Percentage Error
Mean absolute percentage error is measure of accuracy in a fitted time series value in statistics, specifically trending. It usually expresses accuracy as a percentage.... Mean and predicted response
Mean and predicted response
In linear regression mean response and predicted response are values of the dependent variable calculated from the regression parameters and a given value of the independent variable....
Mean deviation
Mean difference
Mean difference
The mean difference is a Statistical_dispersion#Measures_of_statistical_dispersion equal to the average absolute difference of two independent values drawn from a probability distribution.... Mean integrated squared error
Mean integrated squared error
In statistics, the mean integrated squared error is used in density estimation. The MISE of an estimator of an unknown probability density is given by... Mean of circular quantities
Mean of circular quantities
In mathematics, a mean of circular quantities is a mean which is suited for quantities like angles, daytimes, and fractional parts of real numbers.... Mean reciprocal rank
Mean reciprocal rank
Mean reciprocal rank is a statistic for evaluating any process that produces a list of possible responses to a query, ordered by probability of correctness.... Mean square quantization error
Mean square quantization error
Mean square quantization error is a figure of merit for the process of Analog-to-digital converter.As the input is varied, the input's value is recorded when the digital output changes.... Mean square weighted deviation
Mean square weighted deviation
Mean square weighted deviation is used extensively in geochronology, the science of obtaining information about time from rocks.Often the geochronologist will make a determine a sequence of measured ages, with the measured value having a weighting and an associated error associated with each determination.... Mean squared error
Mean squared error
In statistics, the mean squared error or MSE of an estimator is one of many ways to quantify the amount by which an estimator differs from the true value of the quantity being estimated.... Mean squared prediction error
Mean squared prediction error
In statistics the mean squared prediction error of a smoothing procedure is the expected sum of squared deviations of the fitted values from the function ....
Mean time between failures
Mean-reverting process — redirects to Ornstein–Uhlenbeck process
Measurement, level of — see level of measurement
Level of measurement
The "levels of measurement" is an expression which typically refers to the theory of scale types developed by the Harvard psychologist Stanley Smith Stevens.... .
Median
Median
In probability theory and statistics, a median is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half.... Median absolute deviation
Median absolute deviation
In statistics, the median absolute deviation is a Robust statistics measure of the statistical dispersion of a univariate sample.For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median absolute deviation from the median:... Median polish
Median polish
The median polish is an exploratory data analysis procedure proposed by the statistician John Tukey. It finds an additively-fit model for data in a two-way layout table of the form row effect + column effect + overall median.... Median test
Median test
In statistics, Mood's median test is a special case of Pearson's chi-square test. It is a nonparametric test that tests the null hypothesis that the medians of the Statistical populations from which two Sampling are drawn are identical.... Mediation (statistics)
Mediation (Statistics)
In statistics, a mediation model is one that seeks to identify and explicate the mechanism that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third explanatory variable, known as a mediator variable.... Medical statistics
Medical statistics
Medical statistics deals with applications of biostatistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research.... Memorylessness
Memorylessness
In probability theory, memorylessness is a property of certain probability distributions: the exponential distributions and the geometric distributions, wherein any derived probability from a set of random samples is distinct and has no information of earlier samples.... Mentor (statistics)
Mentor (statistics)
Mentor is a flexible and sophisticated statistical package produced by CfMC. It specialises in the Cross tabulation and graphical display of market research and opinion poll data, and is integrated with their Survent data collection software.... – software
Meta-analysis
Meta-analysis
In statistics, a meta-analysis combines the results of several studies that address a set of related research hypotheses. This is normally done by identification of a common measure of effect size, which is modelled using a form of meta-regression.... Meta-analytic thinking
Meta-analytic thinking
Thompson defines meta-analytic thinking as, "a) the prospective formulation of study expectations and design by explicitly invoking prior effect size measures and b) the retrospective interpretation of new results, once they are in hand, via explicit, direct comparison with the prior effect sizes in the related literature."... Method of moments (statistics)
Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. , by equating sample moment with unobservable population moments and then solving those equations for the quantities to be estimated.... Method of simulated moments
Method of simulated moments
In econometrics, the method of simulated moments is a structural estimation technique. It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, like when moment functions involve high-dimensional integrals.... Method of support
Method of support
In statistics, the method of support is a technique that is used to make inferences from datasets.According to A. W. F. Edwards, the method of support aims to make inferences about unknown parameters in terms of the relative support, or log likelihood, induced by a set of data for a particular parameter value....
Metropolis–Hastings algorithm
Mexican paradox
Mexican paradox
The Mexican paradox is the observation that Demographics of Mexico suffer a relatively low incidence of low birth weight, despite having an average socioeconomic status lower that that of peoples of higher or equal socioeconomic status.... Midhinge
Midhinge
In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location parameter.Equivalently, it is the 25% trimmed estimator mid-range; it is an L-estimator....
Mid-range
A Million Random Digits with 100,000 Normal Deviates
A Million Random Digits with 100,000 Normal Deviates
A Million Random Digits with 100,000 Normal Deviates is a 1955 book by the RAND Corporation. The book of tables was an important 20th century work in the field of statistics and random numbers.... (book)
Minimax
Minimax
Minimax is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the maximum possible loss function.... Minimax estimator
Minimax estimator
In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter from observations . An estimator is called minimax if its maximal risk is minimal among all estimators of ....
Minimisation (clinical trials)
Minimum distance estimation
Minimum distance estimation
Minimum distance estimation is a statistical method for fitting a mathematical model to data, usually the Empirical distribution function....
Minimum mean square error
Minimum-variance unbiased estimator
Minimum-variance unbiased estimator
In statistics a uniformly minimum-variance unbiased estimator or minimum-variance unbiased estimator is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.... Minimum viable population
Minimum Viable Population
Minimum viable population is a lower bound on the population of a species, such that it can survive in the wild. This term is used in the fields of biological sciences, ecology, and conservation biology.... Minitab
Minitab
Minitab is a List of statistical packages. It was developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr.... MINQUE
Minque
In statistics, the theory of minimum norm quadratic unbiased estimation was developed by C.R. Rao. Its application was originally to the estimation of variance components in random effects models.... – minimum norm quadratic unbiased estimation
Missing values
Missing values
In statistics, missing values are a common occurrence. Several statistical methods have been developed to deal with this problem. Missing values mean that no data Value is stored for the variable in the current observation.... Mixed logit
Mixed logit
Mixed logit is a fully generalalized, statistical model for approximating utility functions. The inspiration for the mixed logit model came from the limitations of the standard logit, and probit models.... Misuse of statistics
Misuse of statistics
A misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator.... Mixed data sampling
Mixed data sampling
Mixed data sampling is an econometric regression or filtering method developed by Ghysels et al. A simple regression example has the regressor appearing at a higher frequency than the regressand:... Mixed-design analysis of variance
Mixed-design analysis of variance
In statistics, a mixed-design analysis of variance model is used to test for differences between two or more independent groups whilst subjecting participants to repeated measures.... Mixing (mathematics)
Mixing (mathematics)
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.... Mixture density
Mixture density
In statistics, a mixture density is a probability density function which is expressed as a convex combination of other probability density functions.... Mixture model
Mixture model
In mathematics, the term mixture model is a model in which independent variables are fractions of a total.... Mixture (probability)
Mixture (probability)
A mixture is a set of probability distributions often used for statistical classification. An example of use is the mixture model, which creates a data classification hypothesis from a sum of independent distributions.... MLwiN
MLwiN
MLwiN is a statistical software package for fitting multilevel models. It uses both maximum likelihood estimation and Markov Chain Monte Carlo methods.... Mode (statistics)
Mode (statistics)
In statistics, the mode is the value that occurs the most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score.... Model output statistics
Model output statistics
Model Output Statistics is an omnipresent statistics technique that forms the backbone of modern weather forecasting. The technique pioneered in the 1960s and early 1970s is used to post-process output from numerical weather forecast models.... Model selection
Model selection
Model selection is the task of selecting a statistical model from a set of potential models, given data. In its most basic forms, this is one of the fundamental tasks of scientific inquiry.... Moderation (statistics)
Moderation (statistics)
In statistics, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator The effect of a moderating variable is characterized statistically as an interaction .... Moderator variable
Moderator variable
A moderator variable is, in general terms, a Qualitative research or Quantitative research variable that affects the direction and/or strength of the relation between dependent and independent variables.... Modifiable areal unit problem
Modifiable Areal Unit Problem
The modifiable areal unit problem is a source of statistical bias that can radically affect the results of statistical hypothesis tests. MAUP can cause the correlation, or association, between two variables to range from -0.99 to +0.99.... Moment (mathematics)
Moment (mathematics)
The concept of moment in mathematics evolved from the concept of moment in physics. The nth moment of a real-valued function f of a real variable about a value c is... Moment-generating function
Moment-generating function
In probability theory and statistics, the moment-generating function of a random variable X iswherever this expected value exists.The moment-generating function is so called because, if it exists on an open interval around t = 0, then it is the ordinary generating function of the moment of the probability distribution:...
Moments, method of — see method of moments (statistics)
Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. , by equating sample moment with unobservable population moments and then solving those equations for the quantities to be estimated.... Moment problem
Moment problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of Moment s... Monotone likelihood ratio property
Monotone likelihood ratio property
Monotone likelihood ratio property is a property of a family of probability distributions described by their probability density functions .A family of density functions indexed by a parameter taking values in a set is said to have the monotone likelihood ratio in a statistic if for any two parameter values , the ratio is a non-...
Monte Carlo integration
Monte Carlo method
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used when computer simulation physics and mathematics systems.... Monte Carlo method for photon transport
Monte Carlo method for photon transport
Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-tissue interaction and the angles of deflection in a photon's traject...
Monte Carlo methods for option pricing
Monte Carlo methods in finance
Monte Carlo methods in finance
In finance and mathematical finance, Monte Carlo methods are used to value and analyze financial instruments, portfolio s and investments by simulation the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes .... Monte Carlo molecular modeling
Monte Carlo molecular modeling
Monte Carlo molecular modeling is the application of Monte Carlo methods to molecular problems. These problems can also be modeled by the molecular dynamics method.... Moral graph
Moral graph
A moral graph is a concept in graph theory, used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief propagation on graphical models.... Moran's I
Moran's I
Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Like autocorrelation, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated.... Most probable number
Most probable number
The most probable number method, otherwise known as the method of Poisson process zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative data....
Moving average
Moving average model
Moving average model
In time series analysis, the moving average model is common approach for modeling univariate time series models. The notation MA refers to the moving average model of order q:... Multi-armed bandit
Multi-armed bandit
A multi-armed bandit, also sometimes called a K-armed bandit, is a simple machine learning problem based on an analogy with a traditional slot machine but with more than one lever.... Multi-vari chart
Multi-vari chart
In quality control, multi-vari charts are a visual way of presenting variability through a series of charts. The content and format of the charts has evolved over time.... Multicollinearity
Multicollinearity
Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates may change erratically in response to small changes in the model or the data.... Multidimensional analysis
Multidimensional analysis
In statistics, econometrics, and related fields, multidimensional analysis is a data analysis process that groups data into two basic categories: data dimensions and measurements.... Multidimensional panel data
Multidimensional panel data
In econometrics, panel data is data observed over two dimensions . A panel data set is termed "multidimensional" when the phenomenon is observed over three or more dimensions.... Multidimensional scaling
Multidimensional scaling
Multidimensional scaling is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data.... Multilevel model
Multilevel model
Multilevel models are statistical models of parameters that vary at more than one level. These models can be seen as generalizations of linear models, although they can also extend non-linear models.... Multinomial distribution
Multinomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution.The binomial distribution is the probability distribution of the number of "successes" in n statistical independence Bernoulli trials, with the same probability of "success" on each trial.... Multinomial logit
Multinomial logit
In statistics, economics, and genetics, a multinomial logit model is a regression model which generalizes logistic regression by allowing more than two discrete outcomes.... Multinomial probit
Multinomial probit
In econometrics and statistics, the multinomial probit model, a popular alternative to multinomial logit model, is a generalization of the probit model by allowing more than two discrete, unordered outcomes.... Multinomial test
Multinomial test
In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values.... Multiple comparisons
Multiple comparisons
In statistics, the multiple comparisons problem occurs when one considers a set, or family, of statistical inferences simultaneously. Errors in inference, including confidence intervals that fail to include their corresponding population parameters, or hypothesis tests that incorrectly reject the null hypothesis, are more likely when one con... Multiple correlation
Multiple correlation
In statistics, regression analysis is a method for explanation of phenomena and prediction of future events. In the regression analysis, a correlation coefficient r between random variables X and Y is a quantitative index of association between these two variables.... Multiple discriminant analysis
Multiple discriminant analysis
In statistics, multiple discriminant analysis is a generalization of linear discriminant analysis.External links... Multiple-indicator kriging
Multiple-indicator kriging
Multiple-indicator kriging is a recent advance on other techniques for mineral deposit modeling and resource block model estimation, such as ordinary kriging.... Multiple Indicator Cluster Survey
Multiple Indicator Cluster Survey
A Multiple Indicator Cluster Survey is a statistical survey program developed by the UNICEF to provide internationally comparable, statistics rigorous data on the situation of children and woman.... Multiple of the median
Multiple of the median
A multiple of the median is a measure of how far an individual test result deviates from the median. MoM is commonly used to report the results of Screening tests, particularly where the results of the individual tests are highly Statistical dispersion.... Multiple testing correction
Multiple testing correction
Multiple testing correction refers to re-calculating probabilities obtained from a statistical test which was repeated multiple times. Different ways of recalculating include the:... Multiple-try Metropolis
Multiple-try Metropolis
In Markov chain Monte Carlo, the Metropolis?Hastings algorithm can be used to sample from a probability distribution which is difficult to sample from directly.... Multiscale decision making
Multiscale decision making
Multiscale decision making is a newly developed approach in Operations Research that fuses game theory, Multi-agent system influence diagrams, in particular dependency graphs, and Markov decision processes to solve multiscale challenges across organizational, temporal and spatial scales in distributed decision-making network .... Multitrait-multimethod matrix
Multitrait-multimethod matrix
The multitrait-multimethod matrix is an approach to examining Construct Validity developed by Donald T. Campbell and Donald W. Fiske. There are six major considerations when examining a constructs validity through the MTMM matrix, which are as follows:... Multivariate adaptive regression splines
Multivariate adaptive regression splines
Multivariate adaptive regression splines is a form of regression analysis introduced by Jerome Friedman in 1991 . It is a non-parametric regression technique... Multivariate analysis
Multivariate analysis
Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time....
Multivariate analysis of variance
Multivariate distribution – redirects to Joint probability distribution
Multivariate normal distribution
Multivariate normal distribution
In probability theory and statistics, a multivariate normal distribution, sometimes also called a multivariate Gaussian distribution, is a generalization of the one-dimensional normal distribution to higher dimensions.... Multivariate Polya distribution
Multivariate Polya distribution
The multivariate George Polya distribution, also called the Dirichlet compound multinomial distribution, is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and a set of discrete samples x is drawn from the multinomial distribution with probabili... Multivariate probit
Multivariate probit
In statistics and econometrics, the multivariate probit model is a generalization of the probit model used to estimate several correlated binary outcomes jointly.... Multivariate random variable
Multivariate random variable
A multivariate random variable or random vector is a vector space X = whose components are scalar -valued random variables on the same probability space .... Multivariate statistics
Multivariate statistics
Multivariate statistics or multivariate analysis in statistics describes a collection of procedures which involve observation and statistical analysis of more than one statistical variable at a time.... Multivariate Student distribution
Multivariate Student distribution
In statistics, a multivariate Student distribution is a multivariate generalization of the Student's t-distribution. One common method of construction, for the case of dimensions, is based on the observation that if and are independent and distributed as and respectively, is a p x p matrix, and , then has the density...
A naive Bayes classifier is a term in Bayesian statistics statistics dealing with a simple probabilistic Classifier based on applying Bayes' theorem with strong statistical independence assumptions.... Nakagami distribution
Nakagami distribution
The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. It has two parameters: a shape parameter ? and a second parameter controlling spread, ?.... National and international statistical services
List of national and international statistical services
A natural or Quasi-experiment is a naturally occurring instance of observable phenomena which approximate or duplicate the properties of a controlled experiment.... Natural exponential family
Natural exponential family
In probability and statistics, a natural exponential family is a class of probability distributions that is a special case of an exponential family .... Natural process variation
Natural process variation
Natural process variation, sometimes just called process variation, is the statistics description of natural fluctuations in process outputs.... Negative binomial distribution
Negative binomial distribution
In probability and statistics the negative binomial distribution is a discrete probability distribution. It can be used to describe the distribution arising from an experiment consisting of a sequence of independent trials, subject to several constraints.... Negative predictive value
Negative predictive value
The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed.... Negative relationship
Negative relationship
In statistics, a relationship between two variables is negative if the slope in a corresponding graph is negative, or—what is in some contexts equivalent—if the correlation between them is negative.... Negentropy
Negentropy
The negentropy, also negative entropy or syntropy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life.... Nelson rules
Nelson rules
Nelson rules are a method in process control of determining if some measured variable is out of control . Rules, for detecting "out-of-control" or non-random conditions were first postulated by Walter A.... Nested case-control study
Nested case-control study
A nested case-control study is a type of study design where new case controls are applied into cohorts that were defined before the study begins.... Nested sampling algorithm
Nested sampling algorithm
The nested sampling algorithm is a computational approach to the problem of comparing models in Bayesian statistics.Bayes' theorem can be applied to a pair of competing models and for data... Neutral vector
Neutral vector
In statistics, and specifically in the study of the Dirichlet distribution, a neutral vector of random variables is one that exhibits a particular type of statistical independence amongst its elements..... Newcastle–Ottawa scale
Newcastle–Ottawa scale
In statistics, the Newcastle?Ottawa scale is a method for assessing the quality of nonrandomised studies in meta-analysis. The scales allocate stars, maximum of nine, for quality of selection, comparability, exposure and outcome of study participants.... Neyman construction
Neyman construction
Neyman construction is a frequentist method to construct an interval at a confidence level that if we repeat the experiment many times the interval will contain the true value a fraction of the time.... Neyman-Pearson lemma
Neyman-Pearson lemma
In statistics, the Neyman-Pearson lemma states that when performing a statistical hypothesis testing between two point hypotheses H0: ?=?0 and H1: ?=?1, then the likelihood-ratio test which rejects H0 in favour of H1 when... Nominal category
Nominal category
A nominal category or a nominal group is a group of objects or ideas that can be collectively grouped on the basis of shared, arbitrary characteristic.... Noncentral chi distribution
Noncentral chi distribution
In probability theory and statistics, the noncentral chi distribution is a generalization of the chi distribution. If are k independent, normal distribution random variables with means and variances , then the statistic... Noncentral chi-square distribution
Noncentral chi-square distribution
In probability theory and statistics, the noncentral chi-square or noncentral distribution is a generalization of the chi-square distribution.... Noncentral F-distribution
Noncentral F-distribution
In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a generalization of the F-distribution.... Noncentral hypergeometric distributions
Noncentral hypergeometric distributions
In statistics, the hypergeometric distribution is the discrete probability distribution generated by picking colored balls at random from an urn problem without replacement.... Nonlinear autoregressive exogenous model
Nonlinear autoregressive exogenous model
In time series modeling, a nonlinear autoregressive exogenous model is a nonlinear autoregressive model which has exogenous inputs. This means that the model relates the present value of the time series to both:... Nonlinear dimensionality reduction
Nonlinear dimensionality reduction
High-dimensional data, meaning data which requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies on an embedded non-linear manifold within the higher dimensional space.... Nonlinear regression
Nonlinear regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables.... Non-homogeneous Poisson process
Non-homogeneous Poisson process
In probability theory, a non-homogeneous Poisson process is a Poisson process with rate parameter such that the rate parameter of the process is a function of time.... Non-linear least squares
Non-linear least squares
Non-linear least squares is the form of least squares analysis which is used to fit a set of m observations with a model that is non-linear in n unknown parameters .... Non-negative matrix factorization
Non-negative matrix factorization
Non-negative matrix factorization is a group of algorithms in multivariate analysis and linear algebra where a matrix , , is factorized into two matrices, and : ... Non-parametric statistics
Non-parametric statistics
Non-parametric statistics uses distribution free methods which do not rely on assumptions that the data are drawn from a given probability distribution.... Nonparametric regression
Nonparametric regression
Nonparametric regression is a form of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data.... Nonprobability sampling
Nonprobability sampling
sampling is the use of a subset of the population to represent the whole population. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated....
Normal approximation
Normal curve equivalent
Normal curve equivalent
A normal curve equivalent , developed for the United States Department of Education by the RMC Research Corporation,NCE stands for Normal Curve Equivalent and was developed [for] the [US] Department of Education.Normal curve equivalent : A normalized standardized score with a mean of 50 and a standard deviation of 21.06 re... Normal distribution
Normal distribution
The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields.... Normal probability plot
Normal probability plot
The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normal distribution.The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.... – see also rankit
Rankit
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data.... Normal score
Normal score
The term normal score is used with two different meanings in statistics. However, each of them relates to assigning alternative values to data points within a dataset, with the broad intention of creating data values than might have arisen from a standard normal distribution.... – see also rankit
Rankit
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data.... and Z score
Normal variance-mean mixture
Normal variance-mean mixture
In probability theory a normal variance-mean mixture with mixing probability density is the continuous probability distribution of a random variable of the form... Normal-gamma distribution
Normal-gamma distribution
In probability theory and statistics, the normal-gamma distribution is a four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision.... Normal-inverse Gaussian distribution
Normal-inverse Gaussian distribution
The normal-inverse Gaussian distribution is continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution.... Normal-scaled inverse gamma distribution
Normal-scaled inverse gamma distribution
In probability theory and statistics, the normal-scaled inverse gamma distribution is a four-parameter family of multivariate continuous probability distributions.... Normality test
Normality test
In statistics, normality tests are used to determine whether a random variable is normal distribution, or not.... Normalization (statistics)
Normally distributed and uncorrelated does not imply independent
In probability theory, two random variables being correlation does not imply their statistical independence. In some contexts, uncorrelatedness implies at least pairwise independence ....
Notation in probability and statistics
np-chart
Np-chart
In industrial statistics, the np-chart is a type of control chart that is very similar to the p-chart except that the statistic being plotted is a number count rather than a sample proportion of items.... Null distribution
Null distribution
In statistical hypothesis testing, the null distribution is the probability distribution of the test statistic when the null hypothesis is true.... Null hypothesis
Null hypothesis
In statistics, a null hypothesis is a concept which arises in the context of statistical hypothesis testing. A common convention is to use the symbol H0 to denote the null hypothesis.... Null result
Null result
Generally, a null result is a result which is null : that is, the proposed result is absent. In science, it is an experimental outcome which does not show an otherwise expected effect....
Nuisance parameter
Nuisance variable
Nuisance variable
Probability In probability theory, a nuisance variable is a random variable which is fundamental to the probabilistic model, but which is of no particular interest in itself.... — redirects to Nuisance parameter
Numerical data
Numerical data
Numerical data is data measured or identified on a numerical scale. Numerical data can be analysed using statistical methods, and results can be displayed using table s, charts, histograms and graph .... Numerical parameter
Numerical parameter
A numerical parameter is an unspecified quantity used in a function that would be completely specified if the parameter were known. Examples include:...
In statistics, observable variables, as opposed to latent variables, are those variables that can be observed and directly measured.... Observational error
Observational error
Observational error is the difference between a measurement value of quantity and its true value. In statistics, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.... Observational study
Observational study
In statistics, an observational study draws inferences about the effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator.... Observed information
Observed information
In Statistics, the Observed Information is the negative of the second derivative of the log-likelihood.... Odds
Odds
In probability theory and statistics the odds in favour of an event or a proposition are the quantity , where p is the probability of the event or proposition.... Odds ratio
Odds ratio
The odds ratio is a measure of effect size, describing the strength of association or non-independence between two binary data values. It is used as a descriptive statistics, and plays an important role in logistic regression.... Official statistics
Official statistics
Official statistics are related directly to the field of statistics and cover all major areas of citizens' lives, such as economic and social development, living conditions , health , education , and the environment .... Ogden tables
Ogden tables
Ogden tables are a set of statistical tables and other information for use in court cases in the UK.Their purpose is to make it easier to calculate future losses in personal injury and fatal accident cases.... Ogive
Omitted-variable bias is the estimator bias that appears in estimates of parameters in a regression analysis when the assumed specification is incorrect, in that it omits an independent variable that should be in the model.... Omnibus test
Omnibus test
Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall.... One-factor-at-a-time method
One-factor-at-a-time method
The one-factor-at-a-time method is a method of design of experiments involving the testing of factors, or causes, one at a time instead of all simultaneously....
One-tailed test — redirects to two-tailed test
Two-tailed test
The two-tailed test is a statistical test used in Statistical inference, in which a given statistical hypothesis testing will be rejected when the value of the statistic is either sufficiently small or sufficiently large.... One-way ANOVA
One-way ANOVA
In statistics, one-way analysis of variance is a technique used to compare means of two or more samples . This technique can be used only for numerical data.... Open-label trial
Open-label trial
An open-label trial or open trial is a type of clinical trial in which both the researchers and participants know which treatment is being administered.... OpenEpi
OpenEpi
OpenEpi is a free, web-based, open source, operating system-independent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data.... – software
OpenBUGS
OpenBUGS
OpenBUGS is a computer software for the Bayesian analysis of Complex system statistical models using Markov chain Monte Carlo methods. OpenBUGS is the open source variant of WinBUGS .... – software
Operational confound
Operational confound
In design of experiments, a subdiscipline of statistics, an operational confound is a type of confound that can occur in both experimental and nonexperimental research designs.... Operational sex ratio
Operational sex ratio
In the evolutionary biology of sexual reproduction, the operational sex ratio is the ratio of sexually competing male to females that are ready to mate.... Operations research
Operations research
Operations Research in the USA, South Africa and Australia, and Operational Research in Europe and Canada, is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.... Opinion poll
Opinion poll
An opinion poll is a statistical survey of public opinion from a particular sampling . Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals.... Optimal decision
Optimal decision
An optimal decision is a decision such that no other available decision options will lead to a better outcome. It is an important concept in decision theory.... Optimal design
Optimal design
In the design of experiments, optimal designs are experimental designs that are generated based on a particular optimality criterion and are generally 'optimal' only for a specified statistical model.... Optimal matching
Optimal matching
Optimal matching is a sequence analysis method used in social science, to assess the dissimilarity of ordered arrays of tokens that usually represent a time-ordered sequence of socio-economic states two individuals have experienced.... Optimal stopping
Optimal stopping
The theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost.... Optimality criterion
Optimality criterion
In statistics, an optimality criterion provides a measure of the fit of the data to a given hypothesis. The selection process is determined by the solution that optimizes the criteria used to evaluate the alternative hypotheses.... Optional stopping theorem
Optional stopping theorem
In probability theory, the optional stopping theorem says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial value .... Order of a kernel
Order of a kernel
The order of a kernel is the first non-zero Moment of a Kernel .... Order of integration
Order of integration
Order of integration, denoted I, is a summary statistics for a time series. It reports the minimum number of differences required to obtain a stationary series.... Order statistic
Order statistic
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rankings, order statistics are among the most fundamental tools in non-parametric statistics and non-parametric inference.... Ordered logit
Ordered logit
In statistics, the ordered logit model , is a regression model for Levels_of_measurement#Ordinal_measurement dependent variables. It can be thought of as an extension of the logistic regression model for dichotomous dependent variables, allowing for more than two response categories.... Ordered probit
Ordered probit
In statistics, ordered probit is a generalization of the popular probit analysis, used for ordinal multinomial dependent variables. Similarly, the popular logit method also has a counterpart ordered logit....
Ordered subset expectation maximization
Ordination (statistics)
Ordination (statistics)
In multivariate statistics, ordination is a method complementary to data clustering, and used mainly in exploratory data analysis . Ordination partially ordered set objects that are characterized by values on multiple variables so that similar objects are near each other and dissimilar objects are further from each other....
Ornstein–Uhlenbeck process
Orthogonal array testing
Orthogonality
Orthogonality
In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle. The word comes from the Greek language ' , meaning "straight", and ' , meaning "angle".... Orthogonality principle
Orthogonality principle
In signal processing, the orthogonality principle is a necessary and sufficient condition for the optimality of a Bayesian estimator. Loosely stated, the orthogonality principle says that the error vector of the optimal estimator is orthogonal to any possible estimator.... Outlier
Outlier
In statistics, an outlier is an observation that is numerically distant from the rest of the data set.They can occur by chance in any distribution, but they are often indicative either of measurement error or that the population has a heavy-tailed distribution.... Outliers ratio
Outliers Ratio
In Video quality, the outliers ratio is a measure of the performance of an objective video quality metric. It is the ratio of "false" scores given by the objective metric to the total number of scores.... Overdispersion
Overdispersion
In statistics, overdispersion is the presence of greater variability in a data set than would be expected based on a given simple statistical model.... Overfitting
Overfitting
In statistics, overfitting is fitting a statistical model that has too many parameters. An absurd and false model may fit perfectly if the model has enough complexity by comparison to the amount of data available.... OxMetrics
OxMetrics
OxMetrics is an econometric software including the Ox programming language for econometrics and statistics, developed by Jurgen Doornik and David Hendry.... – software
In industrial statistics, the p-chart is a type of control chart that monitors the proportion of nonconforming units in a sample. The appropriate data for p-charts are attribute data .... Page's trend test
Page's trend test
In statistics, the Page test for multiple comparisons between ordered correlated variables is the counterpart of Spearman's rank correlation coefficient which summarizes the association of continuous variables.... Paid survey
Paid survey
A paid or incentivized survey is a type of statistical survey where the participant is rewarded through an incentive program, generally entry into a sweepstakes program or a small cash reward, for completing one or more surveys.... Paired comparison analysis
Paired comparison analysis
In paired comparison analysis, also known as paired choice analysis, a range of options are compared and the results are tallied to find an overall winner.... Pairwise independence
Pairwise independence
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are statistical independence.... Panel analysis
Panel analysis
Panel analysis is statistical method, widely used in social science, epidemiology, and econometrics, which deals with two-dimensional panel data.... Panel data
Panel data
In statistics and econometrics, the term panel data refers to two-dimensional data. In marketing, panel data refers to data collected at the point-of-sale .... Panjer recursion
Panjer recursion
The Panjer recursion is an algorithm to compute the probability distribution of a compound random variablewhere both and are stochastic and of a special type.... – a class of discrete compound distributions
Paleostatistics
Paleostatistics
Paleontology often faces phenomena so vast and complex they can be described only through statistics.First applied to the study of a population in 1662 statistics is today a basic tool for natural sciences practitioners, and a solid acquaintance with methods and applications is essential for communication purposes within the scientific community.... Parabolic fractal distribution
Parabolic fractal distribution
In the parabolic fractal distribution, the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank.... PARAFAC
PARAFAC
In statistics, parallel factor analysis also named canonical decomposition or candecomp/parafac decomposition is a multi-way method originating from psychometrics though going back to Hitchcock in 1927.... (Parallel factor analysis)
Parallel factor analysis redirects to PARAFAC
PARAFAC
In statistics, parallel factor analysis also named canonical decomposition or candecomp/parafac decomposition is a multi-way method originating from psychometrics though going back to Hitchcock in 1927.... Paradigm (experimental)
Paradigm (experimental)
In the behavioural sciences, e.g. Psychology, Biology, Neurosciences, an experimental paradigm is an experimental setup that is defined by certain fine-tuned standards and often has a theoretical background.... Parameter identification problem
Parameter identification problem
The parameter identification problem is a problem which can occur in the estimation of multiple-equation econometric models where the equations have variables in common.... Parameter space
Parameter space
In generative art people talk about parameter space as the set of possibleparameters for a generative system.In statistics one can study the Probability distribution of a random variable.... Parametric model
Parametric model
Definition. A set of probability measures on indexed by a parameter is said to be a parametric model or parametric family if and only if the parameter space is a subset of .... Parametric statistics
Parametric statistics
Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inference about the parameters of the distribution.... Pareto analysis
Pareto analysis
Pareto analysis is a statistics technique in decision making that is used for selection of a limited number of tasks that produce significant overall effect.... Pareto distribution
Pareto distribution
The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution that coincides with social sciences, scientific, geophysical, actuarial science, and many other types of observable phenomena.... Pareto index
Pareto index
In economics the Pareto index, named after the Italian economist and sociologist Vilfredo Pareto, is a measure of the breadth of income or wealth distribution.... Pareto interpolation
Pareto interpolation
Pareto interpolation is a method of estimator the median and other properties of a population that follows a Pareto distribution. It is used in economics when analysing the distribution of incomes in a population, when one must base estimates on a relatively small random sample taken from the population.... Pareto principle
Pareto principle
The Pareto principle states that, for many events, roughly 80% of the effects come from 20% of the causes.Business management thinker Dr. Joseph Moses Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed that 80% of the land in Italy was owned by 20% of the population....
Path analysis (statistics)
Partial autocorrelation — redirects to Partial autocorrelation function
Partial autocorrelation function
In time series analysis, the partial autocorrelation function plays an important role in data analyses aimed at identifying autoregressive models and autoregressive moving average models.... Partial autocorrelation function
Partial autocorrelation function
In time series analysis, the partial autocorrelation function plays an important role in data analyses aimed at identifying autoregressive models and autoregressive moving average models.... Partial correlation
Partial correlation
In probability theory and statistics, partial correlation measures the degree of Association between two random variables, with the effect of a set of controlling random variables removed....
Partial least squares
Partial least squares regression
Partial least squares regression
In statistics, the method of partial least squares regression bears some relation to principal component analysis; instead of finding the hyperplanes of minimum variance, it finds a linear model describing some predicted variables in terms of other observable variables....
Partial leverage
Partial regression plot
Partial regression plot
In applied statistics, a partial regression plot attempts to show the effect of adding an additional variable to the model . Partial regression plots are also referred to as added variable plots, adjusted variable plots, and individual coefficient plots.... Partial residual plot
Partial residual plot
In applied statistics, a partial residual plot is a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.... Particle filter
Particle filter
Particle filters, also known as sequential Monte Carlo methods , are sophisticated model estimation techniques based on simulation.They are usually used to estimate Bayesian models and are the Sequential estimation analogue of Markov chain Monte Carlo batch methods and are often similar to importance sampling methods....
Parzen window
Path analysis (statistics)
Path coefficient
Pattern recognition
Pattern recognition
Pattern recognition is a sub-topic of machine learning. It is "the act of taking in raw data and taking an action based on the Category of the data".... Pearson's chi-square test
Pearson's chi-square test
Pearson's chi-squaretest is the best-known of several chi-square tests ? Statistics procedures whose results are evaluated by reference to the chi-square distribution.... (one of various chi-square tests)
Pearson distribution
Pearson distribution
The Pearson distribution is a family of continuous probability distribution probability distributions. It was first published by Karl Pearson in 1895 and subsequently extended by him in 1901 and 1916 in a series of articles on biostatistics.... Pearson product-moment correlation coefficient
Pearson product-moment correlation coefficient
In statistics, the Karl Pearson product-moment correlation coefficient is a common measure of the correlation between two variables X and Y.... People v. Collins
People v. Collins
The People of the State of California v. Collins was a 1968 jury trial in California, USA that made notorious forensic use of mathematics and probability.... (prob/stats related court case)
Per capita
Per capita
Per capita is a Latin phrase meaning per head with per meaning "through" or "by" and capita meaning "heads." Both words together equate to the phrase "for each head."... Per-protocol analysis
Per-protocol analysis
In epidemiology, Per-protocol analysis is in contrast to the Intention to treat analysis. It is a strategy of analysis in which only patients who complete the entire clinical trial or other procedure analyzed, not like the Intention to treat analysis which also includes the patients who dropped out.... Percentile
Percentile
A percentile is the value of a variable below which a certain percentage of observations fall. So the 20th percentile is the value below which 20 percent of the observations may be found.... Percentile rank
Percentile rank
The percentile rank of a score is the percentage of scores in its frequency distribution which are lower or equal to it. For example, a test score which is greater than or equal to 85% of the scores of people taking the test is said to be at the 85th percentile.... Periodic variation
Periodic variation
In statistics, the periodic variation of a time series is its cyclic variation, either regular or semiregular. See also periodic function.A completely regular cyclic variation in a time series might be dealt with in time series analysis by using a model including one or more sinusoids, where the period-lengths of the sinusoids may be known... Peirce's criterion
Peirce's criterion
Peirce's criterion is a method, devised by Benjamin Peirce, that may be used to eliminate suspect experimental data using probability theory.... Percentage point
Percentage point
Percentage points are the unit for the arithmetic difference of two percentages.Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked.... Phase dispersion minimization
Phase dispersion minimization
Phase dispersion minimization is a data analysis technique that searches for periodic function components of a time series data set. It is useful for data sets with gaps, non-sinusoidal variations, poor time coverage or other problems that would make Fourier transform unusable.... Phase-type distribution
Phase-type distribution
A phase-type distribution is a probability distribution that results from a system of one or more inter-related Poisson processes occurring in sequence, or phases.... Philosophy of probability
Philosophy of probability
The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematics concepts and ordinary language as it is used by non-mathematicians.... Philosophy of statistics
Philosophy of statistics
The philosophy of statistics involves the meaning, justification, utility, use and abuse of statistics and its methodology, and ethical and epistemological issues involved in the consideration of choice and interpretation of data and methods of Statistics.... Pie chart
Pie chart
A pie chart is a circle chart divided into Circular sectors, illustrating relative magnitude or frequencies. In a pie chart, the arc length of each sector , is proportionality to the quantity it represents.... Pignistic probability
Pignistic probability
A pignistic probability is a probability that a rational person will assign to an option when required to make a decision.A person may have, at one level certain beliefs or a lack of knowledge, or uncertainty, about the options and their actual likelihoods....
Pitman-Koopman-Darmois theorem
Pitman closeness
Pivotal quantity
Pivotal quantity
In statistics, a pivotal quantity is a function of observations whose distribution does not depend on unknown parameters.More formally, given an independent and identically distributed sample from a distribution with parameter , a function is a pivotal quantity if the distribution of is independent of .... Placebo-controlled studies
Placebo-controlled studies
A Placebo-controlled study is a way of testing a medical therapy in which, in addition to a group of subjects that receives the treatment to be evaluated, a separate Scientific control group receives a sham "placebo" treatment which is specifically designed to have no real effect.... Plackett-Burman design
Plackett-Burman design
Plackett-Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply.... Plate notation
Plate notation
Plate notation is a method of representing variables that repeat in a graphical model. Instead of drawing each repeated variable individually, a plate or rectangle is used to group variables into a subgraph that repeat together, and a number is drawn on the plate to represent the number of repetitions of the subgraph in the plate.... Player wins
Player wins
Player wins is a stat used to estimate the number of games a player won for his team developed by Dean Oliver , the first full-time statistical analyst in the NBA.... Plot (graphics)
Plot (graphics)
A plot is is a graphical technique for presenting a data set drawn by hand or produced by a mechanical or electronic plotter. It is a graph depicting the relationship between two or more variables used, for instance, in visualising scientific data.... Poincaré plot
Poincaré plot
A Poincar? plot, named after Henri Poincar?, is used to quantify self-similarity in processes, usually periodic functions.Some quotes from the literature:... Point-biserial correlation coefficient
Point-biserial correlation coefficient
The point biserial correlation coefficient is a correlation coefficient used when one variable is dichotomy; Y can either be 'naturally' dichotomous, like gender, or an artificially dichotomized variable.... Point estimation
Point estimation
In statistics, point estimation involves the use of statistical sample data to calculate a single value which is to serve as a "best guess" for an unknown population parameter.... Point process
Point process
In mathematics, a point process is a random element whose values are "point patterns" on a Set S. While in the exact mathematical definition a point pattern is specified as a locally finite counting Measure , it is sufficient for more applied purposes to think of a point pattern as a countable set subset of S that has no limit points... Poisson distribution
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and Statistical independence of the time since the last event.... Poisson hidden Markov model
Poisson hidden Markov model
In statistics, Poisson hidden Markov models are a special case of hidden Markov models where a Poisson process has a rate which varies in association with changes between the different states of a Markov model.... Poisson limit theorem
Poisson limit theorem
The Poisson theorem gives a Poisson distribution approximation to the binomial distribution, under certain conditions. The theorem was named after Simeon Poisson .... Poisson process
Poisson process
A Poisson process, named after the French mathematician Sim?on-Denis Poisson , is the stochastic process in which events occur continuously and memorylessness .... Poisson regression
Poisson regression
In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modelled by a linear combination of unknown parameters....
Poisson random numbers — redirects to section of Poisson distribution
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and Statistical independence of the time since the last event.... Poisson sampling
Poisson sampling
In the theory of finite population sampling, Poisson sampling is a sampling process where each element of the statistical population that is sampled is subjected to an statistical independence Bernoulli trial which determines whether the element becomes part of the sample during the drawing of a single sample.... Polar distribution
Polar distribution
In probability theory, the polar distribution is the probability distribution of angles occurring in a set of two-dimensional vectors, denoted by... Policy capturing
Policy capturing
Policy capturing or "the PC technique" is a very modern and a very often used method or a technique of assessment of one's work or performance at something, whether the one is a someone or something .... Political forecasting
Political forecasting
Political forecasting aims at predicting the outcome of elections. Models include:... Pollyanna Creep
Pollyanna creep
Pollyanna Creep is a phrase that originated with John Williams, a California-based economic analyst and statistician. It describes the way the Federal government of the United States has modified the way important economic measures are calculated with the purpose of giving a better impression of economic development.... Polychoric correlation
Polychoric correlation
In statistics, polychoric correlation is a technique for estimating the correlation between two theorised normal distribution continuous latent variables, from two observed level of measurements.... Polynomial and rational function modeling
Polynomial and rational function modeling
In statistical modeling , polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.... Polynomial chaos
Polynomial chaos
Polynomial chaos is a term created in 1938 by Norbert Wiener, describing a method for representing an unknown variable as a probability distribution.... Pooled standard deviation
Pooled standard deviation
In statistics, pooled standard deviation is a way to find an estimate of the population standard deviation given several different sample taken in different circumstances where the mean may vary between samples but the true standard deviation is assumed to remain the same.... Pooled variance
Pooled variance
In statistics, many times, data are collected for a statistical independence, y, over a range of values for the statistical independence, x. For example, the observation of fuel consumption might be studied as a function of engine speed while the engine load is held constant.... Pooling design
Pooling design
A pooling design is an algorithm to intelligently classify items by testing them in groups or pools rather than individually. The result from the pools is usually binary — either positive or negative.... Population
Statistical population
In statistics, a statistical population is a Set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population.... Population dynamics
Population dynamics
Population dynamics is the branch of life sciences that studies short- and long-term changes in the size and age composition of populations, and the biology and environment processes influencing those changes.... Population ecology
Population ecology
Population ecology is a major sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the natural environment.... – application
Population modeling
Population modeling
Population modeling is an application of statistical models to the study of changes in populations.Models allow us to better understand how complex interactions and processes work.... Population pyramid
Population pyramid
A population pyramid, also called age-sex pyramid and age structure diagram, is a graphical illustration that shows the distribution of various age groups in a population , which normally forms the shape of a pyramid.... Population statistics
Population statistics
Population statistics is the use of Statistics to analyze characteristics or changes to a population. It is related to Social Demography and Demography.... Population viability analysis
Population viability analysis
Population viability analysis is a species-specific method of risk assessment frequently used in conservation biology. It is traditionally defined as the process that determines the probability that a population will go extinct within a given number of years.... Portmanteau test
Portmanteau test
In statistics, a portmanteau test tests whether any of a group of autocorrelations of a time series are different from zero. Among portmanteau tests are both the Ljung-Box test and the Box-Pierce test.... Positive predictive value
Positive predictive value
The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed.... Post-hoc analysis
Post-hoc analysis
Post-hoc analysis Design of experiments and analysis of experiments, refers to looking at the data?after the experiment has concluded?for patterns that were not specified a priori .... Posterior probability
Posterior probability
The posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant Scientific evidence is taken into account.... Power law
Power law
A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases.... Power transform
Power transform
In statistics, the power transform is a family of transformations that map data from one space to another using power functions. This is a useful data processing technique used to reduce data variation, make the data more normal distribution-like, improve the correlation between variables and for other data stabilization procedures.... Prediction interval
Prediction interval
In statistics, a prediction interval bears the same relationship to a future observation that a confidence interval bears to an unobservable population parameter.... Predictive analytics
Predictive analytics
Predictive analytics encompasses a variety of techniques from statistics and data mining that analyze current and historical data to make predictions about future events.... Predictive informatics
Predictive informatics
Predictive informatics is the combination of predictive modeling and informatics applied to healthcare, pharmaceutical, life sciences and business industries.... Predictive modelling
Predictive modelling
Predictive modelling is the process by which a model is created or chosen to try to best predict the probability of an outcome. In many cases the model is chosen on the basis of detection theory to try to guess the probability of a signal given a set amount of input data, for example given an email determining how likely that it is e-mail sp... Predictive validity
Predictive validity
In psychometrics, predictive validity is the extent to which a test score on a scale or test predicts scores on some criterion measure.For example, the Validity of a cognitive test for job performance is the correlation between test scores and, for example, supervisor performance ratings.... Preference regression (in marketing)
Preference regression (in marketing)
Preference regression is a statistical technique used by marketers to determine consumers? preferred core benefits. It usually supplements positioning techniques like multi dimensional scaling or factor analysis and is used to create ideal vectors on perceptual mapping.... Principal components analysis
Principal components analysis
Principal component analysis involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components.... Principal component regression
Principal component regression
In statistics, principal component regression is a regression analysis that uses principal component analysis when estimating regression coefficients.... Principal geodesic analysis
Principal geodesic analysis
In geometric data analysis and statistical shape analysis, principal geodesic analysis is a generalization of principal component analysis to a Euclidean geometry, non-linear setting of manifolds suitable for use with shape descriptors such as medial representations.... Principle of maximum entropy
Principle of maximum entropy
The principle of maximum entropy is a postulate about a universal feature of any probability assignment on a given set of propositions . Let some testable information about a probability distribution function be given.... Prior knowledge for pattern recognition
Prior knowledge for pattern recognition
Pattern recognition is a very active field of research intimately bound to machine learning. Also known as classification or statistical classification, pattern recognition aims at building a classifier that can determine the class of an input pattern.... Prior probability
Prior probability
A prior probability is a conditional probability, interpreted as a description of what is known about a variable in the absence of some Marginal likelihood....
Prior probability distribution redirects to Prior probability
Prior probability
A prior probability is a conditional probability, interpreted as a description of what is known about a variable in the absence of some Marginal likelihood.... Probabilistic design
Probabilistic design
Probabilistic design is a discipline within Engineering Design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase.... Probabilistic forecasting
Probabilistic forecasting
Probabilistic forecasting is a technique for weather forecasting which relies on different methods to establish an event occurrence/magnitude probability.... Probabilistic latent semantic analysis
Probabilistic latent semantic analysis
Probabilistic latent semantic analysis , also known as probabilistic latent semantic indexing is a statistical technique for the analysis of two-mode and co-occurrence data.... Probabilistic metric space
Probabilistic metric space
A probabilistic metric space is a generalization of metric spaces where the distance is no longer defined on positive real numbers, but on distribution functions.... Probabilistic proposition
Probabilistic proposition
A probabilistic proposition is a proposition with a measured probability of being true for an arbitrary person at an arbitrary time.These are some examples of probabilistic propositions collected by the Mindpixel project::* You are not human 0.17 :* Color and colour are the same word spelled differently 0.95 :* You do not think the sun will... Probabilistic relational model
Probabilistic relational model
A Probabilistic relational model is the counterpart of a Bayesian network in statistical relational learning.External links... Probability
Probability
Probability, or wikt:chance, is a way of expressing knowledge or belief that an Event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about t... Probability density function
Probability density function
In mathematics, a probability density function is a function that represents a probability distribution in terms of integrals.Formally, a probability distribution has density ƒ, if ƒ is a non-negative Lebesgue integration function such that the probability of the interval [a, b] is given by... Probability distribution
Probability distribution
In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval .... Probability integral transform
Probability integral transform
In statistics, the probability integral transform or transformation relates to the result that data values that are modelled as being random variables from any given continuous distribution can be converted to random variables having a uniform distribution, provided that the assumption is true.... Probability interpretations
Probability interpretations
The word probability has been used in a variety of ways since it was first coined in relation to games of chance. Does probability measure the real, physical tendency of something to occur, or is it just a measure of how strongly one believes it will occur? In answering such questions, we interpret the probability values of probability theo... Probability mass function
Probability mass function
In probability theory, a probability mass function is a function that gives the probability that a discrete random variable random variable is exactly equal to some value.... Probability matching
Probability matching
Probability matching is a suboptimal decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict a class... Probability metric
Probability metric
A probability metric is a function defining a metric space between random variables or random vector. In particular the probability metric does not satisfy the identity of indiscernibles condition required to be satisfied by the Metric of the metric space.... Probability of error
Probability of error
In statistics, the term "error" arises in two ways. Firstly, it arises in the context of decision making, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error.... Probability plot
Probability plot
A probability plot is a graphical technique for assessing whether or not a data set follows a given distribution such as the normal distribution or Weibull distribution, and for visually estimating the location parameter and scale parameters of the chosen distribution.... Probability plot correlation coefficient plot
Probability plot correlation coefficient plot
Many statistical analysis are based on distributional assumptions about the population from which the data have been obtained. However, distributional families can have radically different shapes depending on the value of the shape parameter.... Probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of Statistical randomness phenomena. The central objects of probability theory are random variables, stochastic processes, and event s: mathematical abstractions of determinism events or measured quantities that may either be single occurrences or evolve over time in an a... Probit
Probit
In probability theory and statistics, the probit function is the inverse function cumulative distribution function , or quantile function associated with the standard normal distribution.... Probit model
Probit model
In statistics, a probit model is a popular specification of a generalized linear model. In particular, it is used for Binomial regression using the probit link function.... Procedural confound
Procedural confound
A procedural confound is a type of confound that can occur in a laboratory experiment or a quasi-experiment. This type of confound occurs when the researcher mistakenly allows another variable to change along with the manipulated independent variable.... Process Window Index
Process Window Index
Process Window Index is a statistical measure that quantifies the robustness of a manufacturing process which involves heating and cooling, known as a thermal process.... Procrustes analysis
Procrustes analysis
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.... Proebsting's paradox
Proebsting's paradox
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing.... Product form solution
Product form solution
In probability theory, a product form solution is a particularly efficient form of solution for determining the equilibrium distribution of a Markov process in cases where it can be written as a product of the equilibrium distributions of sub-components....
Profile likelihood redirects to Likelihood function
Likelihood function
In statistics, the likelihood function is a function of the parameters of a statistical model that plays a key role in statistical inference. In non-technical usage, "likelihood" is a synonym for "probability", but throughout this article only the technical definition is used.... Progressively measurable process
Progressively measurable process
In mathematics, progressive measurability is a property of stochastic processes. A progressively measurable process cannot "see into the future", but being progressively measurable is a strictly stronger property than the notion of being an adapted process.... Prognostics
Prognostics
Prognostics is an engineering discipline focused on predicting the future condition of a component and/or system of components. The science of prognostics is based on the analysis of failure modes, detection of early signs of wear and aging in complex systems and components, and correlation of these signs with an aging profile .... Projection pursuit
Projection pursuit
Projection pursuit is a type of statistical technique which involves finding the most "interesting" possible projections in multidimensional data.... Proof of Stein's example
Proof of Stein's example
Stein's example is an important result in decision theory which can be stated asThe following is an outline of its proof. The reader is referred to the Stein's example for more information.... Propagation of uncertainty
Propagation of uncertainty
In statistics, propagation of uncertainty is the effect of variables' uncertainty on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have Observational error which propagate to the combination of variables in the function.... Propensity score
Propensity score
In the design of experiments, a propensity score is the probability of a unit being assigned to a particular condition in a study given a set of known covariates.... Propensity score matching
Propensity score matching
In statistics, propensity score matching is one of quasi-empirical ?correction strategies? that corrects for the selection biases in making estimates.... Proper linear model
Proper linear model
In statistics, a proper linear model is a linear model in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion.... Proportional hazards models
Proportional hazards models
GeneralProportional hazards models are a sub-class of survival analysis in statistics.For the purposes of this article, consider survival models to consist of two parts: the underlying hazard function, describing how hazard changes over time, and the effect parameters, describing how hazard relates to other factors - such as the choi... Proportional reduction in loss
Proportional reduction in loss
Proportional reduction in loss refers to a general framework for developing and evaluating measures of data reliability . It was proposed by Bruce Cooil and Roland T.... Prosecutor's fallacy
Prosecutor's fallacy
The prosecutor's fallacy is any of several fallacy of statistical reasoning often used in legal arguments. Two of the most common errors are described below:... Proxy (statistics)
Proxy (statistics)
In statistics, a proxy variable is something that is probably not in itself of any great interest, but from which a variable of interest can be obtained.... Psephology
Psephology
Psephology is the statistical analysis of elections. Psephology uses compilations of precinct voting returns for elections going back some years, public opinion polls, campaign finance information and similar statistical data.... Pseudocount
Pseudocount
A pseudocount is a count added to observation data in order to change the probability in a model of those data, which is known not to be 0 , to being negligible rather than being zero.... Pseudolikelihood
Pseudolikelihood
Pseudolikelihood is a measure in statistics that serves as an approximation of the probability distribution of a random variable. Given a set of random variables and a set of dependencies between these random variables, where implies is Conditional independence of given 's neighbors, the pseudolikelihood of is... Pseudomedian
Pseudomedian
In statistics, the pseudomedian is defined as the median of all possible midpoints of pairs of observations. It is the Hodges-Lehmann one-sample estimate of the central location for a distribution.... Pseudoreplication
Pseudoreplication
Pseudoreplication is a source of error in the statistical inferences drawn from experiments or observational study, primarily in the fields of biology and ecology.... PSPP
PSPP
PSPP is a free software application for analysis of sampled data. It has a graphical user interface and conventional command line interface. It is written in C , uses GNU Scientific Library for its mathematical routines, and plotutils for generating graphs.... (free software)
Psychological statistics
Psychological statistics
Psychological statistics is the application of statistics to psychology. Some of the more common applications include:#psychometrics#learning theory ... p-rep
P-rep
P-rep or has been proposed as a statistical alternative to the classic p-value. Whereas a p-value is the probability of obtaining a result under the null hypothesis, p-rep is supposed to represent the probability of replicating an effect.... P-value
P-value
In statistics hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.... Pythagorean expectation
Pythagorean expectation
Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of run they scored and allowed....
lass="link1" onMouseover='showByLink("m876215",this)' onMouseout='hide("m876215")'href="http://www.absoluteastronomy.com/topics/Q_test">Q test
Q test
In statistics, the Q test is used for identification and rejection of outliers. This test should be used sparingly and never more than once in a data set.... Q-Q plot
Q-Q plot
In statistics, a Q-Q plot is a graphical method for diagnosing differences between the probability distribution of a statistical population from which a random sample has been taken and a comparison distribution.... Q-statistic
Q-statistic
The Q-statistic is a test statistic output by either the Box-Pierce test or, in a modified version which provides better small sample properties, by the Ljung-Box test....
Quadratic trend analysis
Quadratic classifier
Quadratic classifier
A quadratic classifier is used in machine learning and statistical classification to separate measurements of two or more classes of objects or events by a quadric surface.... Quadratic form (statistics)
Quadratic form (statistics)
If is a vector space of random variables, and is an -dimensional symmetric square matrix, then the scalar quantity is known as a quadratic form in .... Qualitative comparative analysis
Qualitative comparative analysis
Qualitative Comparative Analysis is a technique, developed by Charles Ragin in 1987, for solving the problems that are caused by making causal inferences on the basis of only a small number of cases....
Qualitative data
Qualitative variation
Qualitative variation
An index of qualitative variation is a measure of statistical dispersion in nominal distributions. There are a variety of these, but they have been relatively little-studied in the statistics literature.... Quantile
Quantile
Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. Dividing ordered data into q essentially equal-sized data subsets is the motivation for q-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets.... Quantile function
Quantile function
In probability theory, a quantile function of aprobability distribution is the inverse function F −1 of its cumulative distribution function F.... Quantile regression
Quantile regression
Quantile regression is a type of regression analysis used in statistics. Whereas the method of least squares results in estimates that approximate the conditional mean of the response variable given certain values of the predictor variables, quantile regression results in estimates approximating either the median or other quantiles of th... Quantitative marketing research
Quantitative marketing research
Quantitative marketing research is the application of quantitative research techniques to the field of marketing. It has roots in both the positivism view of the world, and the modern marketing viewpoint that marketing is an interactive process in which both the buyer and seller reach a satisfying agreement on the "Marketing mix" of marketing... Quantitative parasitology
Quantitative psychological research is defined as psychology research which performs mathematical modeling and statistical estimation or statistical inference.... Quantitative research
Quantitative research
Quantitative research is the systematic scientific investigation of quantitative properties and phenomena and their Causalitys. The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to natural phenomena.... Quartile
Quartile
In descriptive statistics, a quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents one fourth of the sampled population.... Quartile coefficient of dispersion
Quartile coefficient of dispersion
In statistics, the quartile coefficient of dispersion is a descriptive statistic used to make comparisons within and between data sets. The statistic is easily computed using the first and third quartiles for each data set.... Quasi-experimental design
Quasi-experimental design
A quasi-experiment is a scientific research method primarily used in the social sciences. ?Quasi? means likeness or resembling, so therefore quasi-experiments share characteristics of true experiments which seek interventions or treatments.... Quasi-likelihood
Quasi-likelihood
In statistics, quasi-likelihood estimation is one way of allowing for overdispersion, that is, greater variability in the data than would be expected from the statistical model used.... Quasi-maximum likelihood
Quasi-maximum likelihood
When an maximum likelihood estimator is applied to a model which is Specification in ways that do not affect the Consistent estimator of the estimator, it is said to be a quasi-maximum likelihood estimator or QMLE.... Queueing model
Queueing model
In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically.... Queueing theory
Queueing theory
Queueing theory is the mathematical study of waiting lines . The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served by the server at the front of the queue....
Queuing theory in teletraffic engineering
Quota sampling
Quota sampling
In quota sampling, the population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion....
In computing, R is a programming language and software environment for statistics computing and graphics. It is an implementation of the S programming language with lexical scoping semantics inspired by Scheme ....
R programming language
R v Adams
R v Adams
R v Adams was a rape trial in England in 1996 which ousted explicit Bayesian statistics from the reasoning admissible before a jury in DNA cases.... (prob/stats related court case)
Radar chart
Radar chart
A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point.... Rademacher distribution
Rademacher distribution
In probability theory and statistics, the Rademacher distribution, named after Hans_Rademacher is a discrete probability distribution probability distribution which has a 50% chance for either 1 or -1.... Radial basis function network
Radial basis function network
A radial basis function network is an artificial neural network that uses radial basis functions as activation functions. They are used in function approximation, time series prediction, and Control theory.... Raised cosine distribution
Raised cosine distribution
In probability theory and statistics, the raised cosine distribution is a probability distribution supported on the interval []. The probability density function is... Ramsey RESET test
Ramsey reset test
The Ramsey Regression Equation Specification Error Test test is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the estimated values help explain the exogenous variable.... — the Ramsey Regression Equation Specification Error Test
Random assignment
Random assignment
Random assignment or random placement is an experimental technique for assigning subjects to different treatments . The thinking behind random assignment is that by randomizing treatment assignment, then the group attributes for the different treatments will be roughly equivalent and therefore any effect observed between treatment grou...
Random data—see randomness
Randomness
Randomness is a lack of order, purpose, Causality, or predictability. Randomness as defined by Aristotle is the situation, when a choice is to be made which has no logical component by which to determine or make the choice ....
Random effects estimation redirects to Random effects model
Random effects model
Random matrix
Random matrix
In probability theory and statistics, a random matrix is a matrix -valued random variable. Many important properties of physical systems can be represented mathematically as matrix problems.... Random multinomial logit
Random multinomial logit
In statistics and machine learning, random multinomial logit is a technique for statistical classification using repeated multinomial logit analyses via Leo Breiman's random forests.... Random naive Bayes
Random naive Bayes
Random naive Bayes extends the Naive Bayes classifier by adopting the random forest principles: random input selection and random feature selection .... Random permutation statistics
Random permutation statistics
The statistics of random permutations, such as the Permutation group#Examples of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations.... Random sample
Random sample
A sample is a subject chosen from a population for investigation. A random sample is one chosen by a method involving an unpredictable component....
Random sampling
Random sequence
Random sequence
A random sequence is a kind of stochastic process. In short, a random sequence is a sequence of random variables.Random sequences are essential in statistics.... Random variate
Random variate
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values.... Random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalization of a trajectory that consists of taking successive random steps. The results of random walk analysis have been applied to computer science, physics, ecology, economics and a number of other fields as a fundamental Statistical model for random processes in time.... Random walk hypothesis
Random walk hypothesis
The random walk hypothesis is a Finance theory stating that stock market Market price evolve according to a random walk and thus the prices of the stock market cannot be predicted.... Randomization
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population .... Randomized controlled trial
Randomized controlled trial
A randomized controlled trial is a type of scientific experiment most commonly used in testing the efficacy or effectiveness of healthcare Service or health technologies .... Randomized block design
Randomized block design
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups that are similar to one another. Typically, a blocking factor is a source of statistical dispersion that is not of primary interest to the experimenter.... Randomized response
Randomized response
Randomized response is a research method used in structured survey interview. It was firstly proposed by S.L. Warner in 1965, and later modified by B.... Randomness tests
Randomness tests
Randomness tests , in data evaluation, are used to analyze the distribution pattern of a set of data. In stochastic modeling, as in some computer simulations, the expected random input data can be verified to show that tests were performed using randomized data.... Range (statistics)
Range (statistics)
In descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion.... Rank abundance curve
Rank abundance curve
A rank abundance curve is a chart used by ecologists to display indicators of biodiversity -specifically Species_richness and Species_evenness. This is achieved using the relative abundances of different species in a sample.... Rank correlation
Rank correlation
In statistics, rank correlation is the study of relationships between different rankings on the same set of items. A rank correlation coefficient measures the correspondence between two rankings and assesses its significance.... mainly links to two following
*Spearman's rank correlation coefficient
Spearman's rank correlation coefficient
In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter rho or as , is a non-parametric statistics measure of correlation – that is, it assesses how well an arbitrary monotonic function could describe the relationship between two variables, witho...
*Kendall tau rank correlation coefficient
Kendall tau rank correlation coefficient
The Kendall tau rank correlation coefficient is a non-parametric statistic used to measure the degree of correspondence between two rankings and assessing the significance of this correspondence.... Rank product
Rank product
The rank product is a biologically motivated test for the detection of differentially Gene expression genes in replicated DNA microarray experiments.... Rank-size distribution
Rank-size distribution
Rank-size distribution or the rank-size rule describes the remarkable regularity in many phenomena including the distribution of city sizes around the world, sizes of businesses, particle sizes , lengths of rivers, frequencies of word usage, wealth among individuals, etc.... Ranking
Ranking
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second.... Rankit
Rankit
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data.... RANSAC
RANSAC
RANSAC is an abbreviation for "RANdom SAmple Consensus". It is an iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers.... Rao–Blackwell theorem
Rao–Blackwell theorem
In statistics, the Rao?Blackwell theorem is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean squared error criterion or any of a variety of similar criteria....
Rao-Blackwellisation — redirects to *Rao–Blackwell theorem
Rao–Blackwell theorem
In statistics, the Rao?Blackwell theorem is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean squared error criterion or any of a variety of similar criteria.... Rasch model
Rasch model
Rasch models are used for analysing data from assessments to measure things such as abilities, attitudes, and personality traits. For example, they may be used to estimate a student's reading ability from answers to questions on a reading assessment, or the extremity of a person's attitude to capital punishment from responses on a questionnai...
*Polytomous Rasch model
Polytomous Rasch model
The polytomous Rasch model is generalization of the dichotomous Rasch model. It is a measurement model that has potential application in any context in which the objective is to measure a trait or ability through a process in which responses to items are scored with successive integers.... Rasch model estimation
Rasch model estimation
Estimation of a Rasch model is a task that arises in the statistical analysis of data relating to cognitive tests, which is where Rasch models are used.... Ratio distribution
Ratio distribution
A ratio distribution is a statistical distribution constructed as the distribution of the ratio of random variables having two other distributions.... Rayleigh distribution
Rayleigh distribution
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution. It can arise when a two-dimensional vector has elements that are normal distribution, are uncorrelated, and have equal variance.... Raw score
Raw score
In statistics and data analysis, a raw score is an original datum that has not been transformed. This may include, for example, the original result obtained by a student on a Test as opposed to that score after transformation to a standard score or percentile rank or the like.... Realization (probability)
Realization (probability)
In probability and statistics, a realization, or observed value, of a random variable is the value that is actually observed . The random variable itself should be thought of as the process how the observation comes about.... Recall bias
Recall bias
In psychology, recall bias is a type of systematic bias which occurs when the way a statistical survey respondent answers a question is affected not just by the correct answer, but also by the respondent's memory.... Receiver operating characteristic
Receiver operating characteristic
In signal detection theory, a receiver operating characteristic , or simply ROC curve, is a graph of a functionical plot of the Sensitivity vs.... Recurrence period density entropy
Recurrence period density entropy
Recurrence period density entropy is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal.... Recurrence plot
Recurrence plot
In descriptive statistics and chaos theory, a recurrence plot is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space.... Recurrence quantification analysis
Recurrence quantification analysis
Recurrence quantification analysis is a method of nonlinear data analysis for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.... Recursive Bayesian estimation
Recursive Bayesian estimation
Recursive Bayesian estimation is a general probabilistic approach for density estimation an unknown probability density function recursively over time using incoming measurements and a mathematical process model....
Recursive least squares
Recursive partitioning
Recursive partitioning
Recursive partitioning is a statistics method for multivariable analysis.. Recursive partitioning creates a decision tree that strives to correctly classify members of the population based on several dichotomous dependent variables.... Reduced form
Reduced form
In statistics, and particularly in econometrics, the reduced form of a system of equations is the result of solving the system for the endogenous variables.... Reference class problem
Reference class problem
In statistics, the reference class problem is the problem of defining a prior probability by the method of imaginary reference sets. It follows from the elementary foundations of probability theory that there is no unique way of doing this.... Regression analysis
Regression analysis
In statistics, regression analysis is a collective name for techniques for the modeling and analysis of numerical data consisting of values of a dependent variable and of one or more independent variables .... — see also linear regression
Linear regression
In statistics, linear regression is used for two things;Linear regression is a form of regression analysis in which the relationship between one or more independent variables and another variable, called the dependent variable, is modeled by a least squares function, called linear regression equation....
Regression Analysis of Time Series — proprietary software
Regression dilution
Regression dilution
Regression dilution is a statistical phenomenon also known as "attenuation".Consider fitting a straight line for the relationship of an outcome variable y to a predictor variable x, and estimating the gradient of the line.... Regression estimation
Regression estimation
Regression estimation is a technique used to replace missing values in data. The variable with missing data is treated as the dependent variable, while the rest of the cases are treated as independent variables.... Regression fallacy
Regression fallacy
The regressionfallacy is an informal fallacy. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations.... Regression discontinuity
Regression discontinuity
In the design of experiments, regression discontinuity designs are designs that evaluate causal effects of interventions, in which assignment to a treatment is determined at least partly by the value of an observed covariate lying on either side of a fixed threshold.... Regression toward the mean
Regression toward the mean
Regression toward the mean is a principle in statistics that states that if you take a pair of independent measurements from the same distribution, samples far from the mean on the first set will tend to be closer to the mean on the second set, and the farther from the mean on the first measurement, the stronger the effect.... Reification (statistics)
Reification (statistics)
In statistics, reification is the use of an idealized model of a statistical process. The model is then used to make inferences connecting model results, which imperfectly represent the actual process, with experimental observations.... Rejection sampling
Rejection sampling
In mathematics, rejection sampling is a technique used to generate observations from a probability distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm".... Relationships among probability distributions
Relationships among probability distributions
Many statistical distributions have close relationships. Some examples include:* Bernoulli distribution, binomial distribution, and normal distribution....
Relative efficiency redirects to Efficiency (statistics)
Efficiency (statistics)
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the desirability of an estimator or of an experimental design.... Relative risk
Relative risk
In statistics and mathematical epidemiology, relative risk is the risk of an event relative to exposure. Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group.... Relative standard deviation
Relative standard deviation
In probability theory and statistics, the relative standard deviation is the absolute value of the coefficient of variation. It is often expressed as a percentage....
Relative variance — redirects to Relative standard deviation
Relative standard deviation
In probability theory and statistics, the relative standard deviation is the absolute value of the coefficient of variation. It is often expressed as a percentage....
Relativistic Breit–Wigner distribution
Reliability (statistics)
Reliability (statistics)
In statistics, reliability is the consistency of a set of measurements or measuring instrument, often used to describe a Test . This can either be whether the measurements of the same instrument give or are likely to give the same measurement , or in the case of more subjective instruments, such as personality or trait inventories, whether t... Reliability engineering
Reliability engineering
Reliability engineering is an engineering field, that deals with the study of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time.... Reliability theory
Reliability theory
Reliability theory developed apart from the mainstream of probability and statistics. It was originally a tool to help nineteenth centuryMarine insurance and life insurance companies compute profitable rates to charge their customers.... Reliability theory of aging and longevity
Reliability theory of aging and longevity
Reliability theory of aging and longevity is a scientific approach aimed to gain theoretical insights into mechanisms of biological aging and species survival patterns by applying a general theory of systems failure, known as reliability theory....
Rencontres numbers — a discrete distribution
Renewal theory
Renewal theory
Renewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times. Applications include calculating the expected time for a infinite monkey theorem to type the word Macbeth and comparing the long-term benefits of different insurance policies.... Repeated measures design
Repeated measures design
The repeated measures design is also known as a within-subject design. It is a frequently used ANOVA design in which all subjects participate in all conditions of the research experiment .... Replication (statistics)
Replication (statistics)
In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated.... Representation validity
Representation validity
Representation validity is concerned about how well the constructs or abstractions translate intoobservable measures. There are two primary questions to be answered.... Resampling (statistics)
Resampling (statistics)
In statistics, resampling is any of a variety of methods for doing one of the following:# Estimating the precision of sample statistics by using subsets of available data or drawing randomly with replacement from a set of data points ... Rescaled range
Rescaled range
The rescaled range is a statistical measure of the variability of a time series introduced by the British hydrologist Harold Edwin Hurst . Its purpose is to provide an assessment of how the apparent variability of a series changes with the length of the time-period being considered.... Resentful demoralization
Resentful demoralization
Resentful demoralization is an issue in controlled experiments in which those in the control group become resentful of not receiving the experimental treatment.... – experimental design
Residual.
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Statistics
Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data.... that are not already on this list.
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1.96 is the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics. 95% of the area under a normal curve lies within roughly 1.96 standard deviations of the mean, and due to the central limit theorem, this number is therefore used in the construction of approximate 95% confidence interva...
In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables is used to estimate causal relationships when controlled experiments are not feasible....
In statistics, the 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution, almost all values lie within 3 standard deviations of the mean....
A one-hundred-year flood is calculated to be the level of flood water expected to be equaled or exceeded every 100 years on average. The 100-year flood is more accurately referred to as the 1% flood, since it is a flood that has a 1% chance of being equaled or exceeded in any single year....
The term a priori probability is used in distinguishing the ways in which values for probabilities can be obtained. In particular, an "a priori probability" is derived purely by deductive reasoning....
Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence....
In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is a measure of central tendency, most often the median or sometimes the mean of the data set....
An ABX test is a method of comparing two kinds of sensory stimuli to identify detectable differences. A subject is presented with two known samples ....
In the statistics area of survival analysis, an accelerated failure time model is a parametric statistics model that provides an alternative to the commonly-used proportional hazards models....
The acceptable quality limit is the worst-case quality level, in percentage or ratio, that is still considered acceptable: that is, it is at an acceptable quality level....
Accidental sampling is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand....
In the fields of science, engineering, industry and statistics, accuracy is the degree of closeness of a Measure d or calculated quantity to its actual Value ....
The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy....
Acquiescence bias is a category of response bias in which respondents to a Sample survey have a tendency to agree with all the questions or to indicate a positive connotation....
Actuarial science is the discipline that applies mathematics and statistics methods to Risk assessment in the insurance and finance industries. Actuary are professionals who are qualified in this field through education and experience....
Adapa or Adamu son of Ea was a Sumerian and Babylonian mythical figure who accidentally rejected the gift of immortality. The story is first attested in the Kassites period .... – software
In the study of stochastic processes, an adapted process is one that cannot "see into the future". An informal interpretation is that X is adapted if and only if, for every realisation and every n, Xn is known at time n....
In the field of statistical language modeling and statistics, additive smoothing is a technique used to smooth a distribution p representing, for example, occurrences of a word x in a text....
ADMB or AD Model Builder is a free software suite for Non-linear statistics Computer_model. It was created by Dave Fournier and now being developed by the ADMB Project, a creation of the non-profit ADMB Foundation.... – software
In classical decision theory, an admissible decision rule is a rule for making a decision that is "better" than any other rule that may compete with it, in a specific sense defined below: it is a maximal element with respect to the below defined partial order....
In epidemiology and demography, Age adjustment, also called age standardisation, is a technique used to better allow populations to be compared when the age profiles of the populations are quite different....
Age-standardized mortality rates are used to compare the mortality rates of places without being skewed by the difference in age distributions from place to place....
In statistics, aggregate data describes data combined from several measurements.In economics, aggregate data or data aggregates describes high-level data that is composed of a multitude or combination of other more individual data....
An Aggregate pattern can refer to concepts in either statistics or computer programming. Both uses deal with considering a large case as composed of smaller, simpler, pieces....
Akaike's information criterion, developed by Hirotsugu Akaike under the name of "an information criterion" in 1971 and proposed in Akaike , is a measure of the goodness of fit of an estimated statistical model....
Algebraic statistics is a fairly recent field of statistics which utilizes the tools of algebraic geometry and commutative algebra in order to study problems related to discrete random variables with finite state spaces....
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst....
Algorithms for calculating variance play a major role in statistics computing. A key problem in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values....
