Irénée-Jules Bienaymé

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Irénée-Jules Bienaymé
Bienaymé–Chebyshev inequality
Bienaymé formula
Scientific career
FieldsStatistics

Irénée-Jules Bienaymé (French:

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[according to whom?] that began with Blaise Pascal and Pierre de Fermat, then continued with Pierre-Simon Laplace and Siméon Denis Poisson. After Bienaymé, progress in statistics took place in the United Kingdom and Russia.

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

Bonapartists
.

In 1818, he lectured on mathematics at 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

Napoléon III
.

In 1852 he was admitted to 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.[1]

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

Bienaymé–Chebyshev inequality which gives a simple demonstration of the law of large numbers. He corresponded with Adolphe Quetelet, and also had links with Gabriel Lamé
.

Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with

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.[2]

References

  1. ISBN 978-0-85729-114-1
    , retrieved 2022-11-28
  2. doi:10.1093/biomet/61.2.375
    .
  • « 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
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