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 scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...

generalizing his

least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

method. He contributed to the fields of

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

and

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, and to their application to

finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

demography Demography () is the statistics, statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and Population dynamics, dynamics of populations; it can cover whole societies or groups ...

and

social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...

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 expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...

of a sum of uncorrelated random variables.

Biography

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

Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pa ...

and

Pierre de Fermat Pierre de Fermat (; between 31 October and 6 December 1607 – 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 ...

, then continued with

Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...

and

Siméon Denis Poisson Baron Siméon Denis Poisson FRS FRSE (; 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, electri ...

. After Bienaymé, progress in statistics took place in the

United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales and North ...

and

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

. 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 in central Paris. It was founded in the ...

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

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

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

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. He spent twenty-three years in ...

because of their sympathy for

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

. In 1818, he lectured on mathematics at the

Saint-Cyr Military Academy Saint-Cyr refers to the popular child-saint Saint Quiricus (Cyriacus), 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 Franc ...

but, two years later, he entered the

Finance Ministry A finance minister is an executive or cabinet position in charge of one or more of government finances, economic policy and financial regulation. A finance minister's portfolio has a large variety of names around the world, such as "treasury", " ...

. 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 may refer to: * Sorbonne (building), historic building in Paris, which housed the University of Paris and is now shared among multiple universities. *the University of Paris (c. 1150 – 1970) *one of its components or linked institution, ...

, 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 the first President of France (as Louis-Napoléon Bonaparte) from 1848 to 1852 and the last monarch of France as Emperor of the French from 1852 to 1870. A nephew ...

. In 1852 he was admitted to the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

. 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 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 SA. Lactalis is the largest dairy products group in the world, and is the sec ...

, 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 and render an impartial verdict (a finding of fact on a question) officially submitted to them by a court, or to set a penalty or judgment. Juries developed in England dur ...

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

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. Chebyshe ...

, 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 (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials shou ...

. He corresponded with

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

, 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 Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He w ...

. 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 model (with fixed level-one effects of a linear function of a set of explanatory variables) by the prin ...

is the

best linear unbiased estimator Best or The Best may refer to: People * Best (surname), people with the surname Best * Best (footballer, born 1968), retired Portuguese footballer Companies and organizations * Best & Co., an 1879–1971 clothing chain * Best Lock Corporation, ...

, 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, there ...

and

homoscedastic In statistics, a sequence (or a vector) of random variables is homoscedastic () if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The s ...

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

Cauchy distribution The Cauchy distribution, named after Augustin 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) fun ...

to show a case where the method of

resulted in a perfectly

inefficient Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...

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

. 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 In mathematics, the witch of Agnesi () is a cubic plane curve defined from two diametrically opposite points of a circle. It gets its name from Italian mathematician Maria Gaetana Agnesi, and from a mistranslation of an Italian word for a sail ...

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