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Gompertz-Makeham law of mortality

 

 
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Gompertz-Makeham law of mortality
 
 
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The Gompertz-Makeham law states that death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.) the age-independent mortality component is often negligible, and in this case the formula simplifies to a Gompertz law of mortality (proposed by Benjamin Gompertz
Benjamin Gompertz

Benjamin Gompertz , was a autodidact mathematician, denied admission to university because he was Jewish. Nevertheless he was made Fellow of the Royal Society in 1819....
 in 1825) with exponential increase
Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportionality to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay ....
 in death rates with age.

The Gompertz-Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window of about 30-80 years.






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The Gompertz-Makeham law states that death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.) the age-independent mortality component is often negligible, and in this case the formula simplifies to a Gompertz law of mortality (proposed by Benjamin Gompertz
Benjamin Gompertz

Benjamin Gompertz , was a autodidact mathematician, denied admission to university because he was Jewish. Nevertheless he was made Fellow of the Royal Society in 1819....
 in 1825) with exponential increase
Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportionality to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay ....
 in death rates with age.

The Gompertz-Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window of about 30-80 years. At more advanced ages the death rates do not increase as fast as predicted by this mortality law - a phenomenon known as the late-life mortality deceleration.

Historical decline in human mortality
Mortality rate

Mortality rate is a measure of the number of deaths in some population, scaled to the size of that population, per unit time. Mortality rate is typically expressed in units of deaths per 1000 individuals per year; thus, a mortality rate of 9.5 in a population of 100,000 would mean 950 deaths per year in that entire population....
 before 1950s was mostly due to decrease in the age-independent mortality component (Makeham parameter), while the age-dependent mortality component (the Gompertz function) was surprisingly stable in history before 1950s. After that a new mortality trend has started leading to unexpected decline in mortality rates at advanced ages and 'de-rectangularization' of the survival curve.

In terms of 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....
 the Gompertz-Makeham law of mortality represents a failure law, where the hazard rate is a mixture of non-aging failure distribution, and the aging failure distribution with exponential increase in failure rates.

The Gompertz law is the same as a 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....
 for the negative of age, restricted to negative values for the random variable
Random variable

In mathematics, random variables are used in the study of Randomness and probability. They were developed to assist in the analysis of Game of chance, stochastic events, and the results of experiment by capturing only the mathematical properties necessary to answer probability questions....
 (positive values for age).

See also

  • Ageing
    Ageing

    Ageing or aging is the accumulation of changes in an organism or object over time. Aging in humans refers to a multidimensional process of physical, psychological, and social change....
  • Biodemography
    Biodemography

    Biodemography is the science dealing with the integration of biology and demography.Biodemography is a new branch of human demography concerned with understanding the complementary biological and demographic determinants of and interactions between the birth and death processes that shape individuals, cohorts and populations....
  • Biodemography of human longevity
    Biodemography of human longevity

    Biodemography is a multidisciplinary approach, integrating biological knowledge with demographic research on human longevity and survival. Biodemographic studies are important for understanding the driving forces of the current longevity revolution , forecasting the future of human longevity, and identification of new strategies for further inc...
  • Biogerontology
    Gerontology

    Gerontology is the study of the social, Psychology and Biology aspects of Ageing. It is distinguished from geriatrics, which is the branch of medicine that studies the disease of the elderly....
  • Demography
    Demography

    Demography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space ....
  • Gompertz curve
    Gompertz curve

    A Gompertz curve or Gompertz function, named after Benjamin Gompertz, is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period....
  • 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....
  • Maximum life span
    Maximum life span

    Maximum life span is a measure of the maximum amount of time one or more members of a group has been observed to survive between birth and death....
  • Mortality
    Mortality rate

    Mortality rate is a measure of the number of deaths in some population, scaled to the size of that population, per unit time. Mortality rate is typically expressed in units of deaths per 1000 individuals per year; thus, a mortality rate of 9.5 in a population of 100,000 would mean 950 deaths per year in that entire population....
  • 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....


Further reading