World Library  
Flag as Inappropriate
Email this Article

Irénée-Jules Bienaymé

Article Id: WHEBN0016087441
Reproduction Date:

Title: Irénée-Jules Bienaymé  
Author: World Heritage Encyclopedia
Language: English
Subject: Variance, Cauchy distribution, List of statisticians
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Irénée-Jules Bienaymé

Irénée-Jules Bienaymé
Irénée-Jules Bienaymé
Born (1796-08-28)28 August 1796
Paris
Died 19 October 1878(1878-10-19) (aged 82)
Paris
Nationality French
Fields Statistics
Known for Bienaymé–Chebyshev inequality
Bienaymé formula

Irénée-Jules Bienaymé (28 August 1796 – 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields of 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.

Biography

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

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 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 Russian mathematician Pafnuty Chebyshev, 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. Both Bienaymè 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 is the best linear unbiased estimator provided errors are uncorrelated and homoscedastic. At the time, this was not known. Cauchy developed the Cauchy distribution to show a case where the method of ordinary least squares resulted in a perfectly inefficient estimator. 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.[1]

References

  1. ^
  • « 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

  • .
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.