Irénée-Jules Bienaymé
Encyclopedia
Irénée-Jules Bienaymé was a French
statistician. He built on the legacy of Laplace
generalizing his least squares
method. He contributed to the fields and probability
, and statistics
and to their application to finance
, demography
and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance
of a sum of uncorrelated random variables.
and Fermat
, then continued with Laplace
and Poisson
. After Bienaymé, progress in statistics took place in the UK and Russia
.
His personal life was marked by bad fortune. He studied at the Lycée de Bruges and then at the Lycée Louis-le-Grand
in Paris. After participating in the defense of Paris in 1814, he attended the École Polytechnique
in 1815. Unfortunately that year's class was excluded in the following year by Louis XVIII because of their sympathy for Bonapartists.
In 1818, he lectured on mathematics at the Académie militaire de Saint-Cyr but, two years later, he entered the Finance Ministry. He was rapidly promoted, first to inspector, then to inspector general. But the new Republican administration removed him in 1848 for his lack of support for the Republican regime.
He became professor of probability at the Sorbonne
, but he lost his position in 1851. He then became a consultant as an expert statistician for the government of Napoléon III.
In 1852 he was admitted to the Académie des sciences. After 23 years, Bienaymé became the examiner for the attribution of the academy's prize in statistics. He was also a founding member of the Société Mathématique de France
, holding its presidency in 1875.
. In particular he studied the extinction of closed families (aristocratic families for instance) which declined even as the general population was growing.
As a disciple of Laplace and under the influence of Laplace's Théorie analytique des probabilités (1812), he defended the latter's conceptions in a debate with Poisson
on the size of juries and on the necessary majority for obtaining a conviction.
He translated into French the works of his friend the Russia
n mathematician Pafnuty Chebychev, and published the Bienaymé-Chebyshev inequality which gives a simple demonstration of the law of large numbers
. He corresponded with Quételet, and also had links with Lamé
.
Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Cauchy
.
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...
statistician. He built on the legacy of Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
generalizing his least squares
Least squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
method. He contributed to the fields and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and to their application to finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, demography
Demography
Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...
and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
of a sum of uncorrelated random variables.
Biography
With Irénée-Jules Bienaymé ends the line of great French probability thinkers that began with PascalBlaise Pascal
Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...
and Fermat
Pierre de Fermat
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality...
, then continued with Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
and Poisson
Siméon Denis Poisson
Siméon Denis Poisson , was a French mathematician, geometer, and physicist. He however, was the final leading opponent of the wave theory of light as a member of the elite l'Académie française, but was proven wrong by Augustin-Jean Fresnel.-Biography:...
. After Bienaymé, progress in statistics took place in the UK and Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
.
His personal life was marked by bad fortune. He studied at the Lycée de Bruges and then at the Lycée Louis-le-Grand
Lycée Louis-le-Grand
The Lycée Louis-le-Grand is a public secondary school located in Paris, widely regarded as one of the most rigorous in France. Formerly known as the Collège de Clermont, it was named in king Louis XIV of France's honor after he visited the school and offered his patronage.It offers both a...
in Paris. After participating in the defense of Paris in 1814, he attended the École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
in 1815. Unfortunately that year's class was excluded in the following year by Louis XVIII because of their sympathy for Bonapartists.
In 1818, he lectured on mathematics at the Académie militaire de Saint-Cyr but, two years later, he entered the Finance Ministry. He was rapidly promoted, first to inspector, then to inspector general. But the new Republican administration removed him in 1848 for his lack of support for the Republican regime.
He became professor of probability at the Sorbonne
Sorbonne
The Sorbonne is an edifice of the Latin Quarter, in Paris, France, which has been the historical house of the former University of Paris...
, but he lost his position in 1851. He then became a consultant as an expert statistician for the government of Napoléon III.
In 1852 he was admitted to the Académie des sciences. After 23 years, Bienaymé became the examiner for the attribution of the academy's prize in statistics. He was also a founding member of the Société Mathématique de France
Société Mathématique de France
The Société Mathématique de France is the main professional society of French mathematicians.The society was founded in 1872 by Émile Lemoine and is one of the oldest mathematical societies in existence...
, holding its presidency in 1875.
Contributions to mathematics
Bienaymé published only 23 articles, half of which appeared in obscure conditions. His first works concerned demographics and actuarial tablesLife table
In actuarial science, a life table is a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday...
. In particular he studied the extinction of closed families (aristocratic families for instance) which declined even as the general population was growing.
As a disciple of Laplace and under the influence of Laplace's Théorie analytique des probabilités (1812), he defended the latter's conceptions in a debate with Poisson
Siméon Denis Poisson
Siméon Denis Poisson , was a French mathematician, geometer, and physicist. He however, was the final leading opponent of the wave theory of light as a member of the elite l'Académie française, but was proven wrong by Augustin-Jean Fresnel.-Biography:...
on the size of juries and on the necessary majority for obtaining a conviction.
He translated into French the works of his friend the Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician Pafnuty Chebychev, and published the Bienaymé-Chebyshev inequality which gives a simple demonstration of the law of large numbers
Law of large numbers
In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...
. He corresponded with Quételet, and also had links with Lamé
Gabriel Lamé
Gabriel Léon Jean Baptiste Lamé was a French mathematician.-Biography:Lamé was born in Tours, in today's département of Indre-et-Loire....
.
Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Cauchy
Augustin Louis Cauchy
Baron Augustin-Louis Cauchy was a French mathematician who was an early pioneer of analysis. He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner, rejecting the heuristic principle of the generality of algebra exploited by earlier authors...
.