Irénée-Jules Bienaymé (; 28 August 1796 – 19 October 1878) was a French statistician. He built on the legacy of

Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

generalizing his

least squares The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The me ...

method. He contributed to the fields of

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

and

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, and to their application to

finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

demography Demography () is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analysis examine ...

and

social science Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...

s. In particular, he formulated the Bienaymé–Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

of a sum of uncorrelated random variables.

Biography

Irénée-Jules Bienaymé continues the line of great French probability thinkers that began with

Blaise Pascal Blaise Pascal (19June 162319August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. Pascal was a child prodigy who was educated by his father, a tax collector in Rouen. His earliest ...

and

Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d ...

, then carried on with

Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...

and

Siméon Denis Poisson Baron Siméon Denis Poisson (, ; ; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity ...

. His personal life was marked by bad fortune. He studied at the Lycée de Bruges and then at the

Lycée Louis-le-Grand The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on Rue Saint-Jacques (Paris), rue Saint-Jacques in central Par ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. After participating in the defense of Paris in 1814, he attended the

École Polytechnique (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...

in 1815. Unfortunately that year's class was excluded in the following year by

Louis XVIII Louis XVIII (Louis Stanislas Xavier; 17 November 1755 – 16 September 1824), known as the Desired (), was King of France from 1814 to 1824, except for a brief interruption during the Hundred Days in 1815. Before his reign, he spent 23 y ...

because of their sympathy for

Bonapartists Bonapartism () is the political ideology supervening from Napoleon Bonaparte and his followers and successors. The term was used in the narrow sense to refer to people who hoped to restore the House of Bonaparte and its style of government. In ...

. In 1818, he lectured on mathematics at the

Saint-Cyr Military Academy Saint-Cyr refers to the popular child-saint Cyricus, whose following was strong in France because relics were brought back from Antioch by the 4th-century Bishop Saint Amator of Auxerre. Saint-Cyr may refer to: Places France * École spécia ...

but, two years later, he entered the

Finance Ministry A ministry of finance is a ministry or other government agency in charge of government finance, fiscal policy, and financial regulation. It is headed by a finance minister, an executive or cabinet position . A ministry of finance's portfolio ...

. 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 Napoleon III (Charles-Louis Napoléon Bonaparte; 20 April 18089 January 1873) was President of France from 1848 to 1852 and then Emperor of the French from 1852 until his deposition in 1870. He was the first president, second emperor, and last ...

. In 1852 he was admitted to the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

. 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 Groupe Lactalis S.A. (doing business as Lactalis) is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier S.A. Lactalis is the largest dairy pr ...

, 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 tables. 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

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 A jury is a sworn body of people (jurors) convened to hear evidence, make findings of fact, and render an impartial verdict officially submitted to them by a court, or to set a penalty or judgment. Most trial juries are " petit juries", an ...

and on the necessary majority for obtaining a conviction. He translated into French the works of his friend the

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

n mathematician

Pafnuty Chebyshev Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebysh ...

, and published the Bienaymé–Chebyshev inequality which gives a simple demonstration of the

law of large numbers In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law o ...

. He corresponded with

Adolphe Quetelet Lambert Adolphe Jacques Quetelet FRSF or FRSE (; 22 February 1796 – 17 February 1874) was a Belgian- French astronomer, mathematician, statistician and sociologist who founded and directed the Brussels Observatory and was influential ...

, and also had links with

Gabriel Lamé Gabriel Lamé (22 July 1795 – 1 May 1870) was a French mathematician who contributed to the theory of partial differential equations by the use of curvilinear coordinates, and the mathematical theory of elasticity (for which linear elasticity ...

. Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Augustin Louis Cauchy. Both Bienaymé and Cauchy published regression methods at about the same time. Bienaymé had generalized the method of ordinary least squares. The dispute within the literature was over the superiority of one method over the other. It is now known that

ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression In statistics, linear regression is a statistical model, model that estimates the relationship ...

is the best linear unbiased estimator, provided errors are

uncorrelated In probability theory and statistics, two real-valued random variables, X, Y, are said to be uncorrelated if their covariance, \operatorname ,Y= \operatorname Y- \operatorname \operatorname /math>, is zero. If two variables are uncorrelated, ther ...

and homoscedastic. At the time, this was not known. Cauchy developed the

Cauchy distribution The Cauchy distribution, named after Augustin-Louis Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) ...

to show a case where the method of

resulted in a perfectly inefficient

estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on Sample (statistics), observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguish ...

. This is due to the fact that the Cauchy distribution has no defined variance to minimize. This is the first direct appearance of the Cauchy distribution in the academic literature. The curve had been previously studied by others, though in the English language as the

Witch of Agnesi Witchcraft is the use of magic by a person called a witch. Traditionally, "witchcraft" means the use of magic to inflict supernatural harm or misfortune on others, and this remains the most common and widespread meaning. According to ''Enc ...

References

*« ''Actes de la journée du 21 juin 1996 consacrée à Irénée-Jules Bienaymé'' », 'Cahiers du Centre d'Analyse et de Mathématiques Sociales', n° 138, ''Série Histoire du Calcul des Probabilités et de la Statistique,'' n° 28, Paris, E.H.E.S.S.-C.N.R.S *Stephen M. Stigler (1974) ''Studies in the history of probability and statistics. XXXIII: Cauchy and the witch of Agnesi: An historical note on the Cauchy distribution.'' Biometrika Vol. 61 No. 2 pp. 375–380

External links

* {{DEFAULTSORT:Bienayme, Irenee-Jules 1796 births 1878 deaths French statisticians École Polytechnique alumni Members of the French Academy of Sciences Lycée Louis-le-Grand alumni Mathematical statisticians