Bienaymé, Jules

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Bienaymé, Jules



Jules Bienaymé, statistician and mathematician, was born in Paris in 1796 and died there in 1878. He received his secondary education in Bruges and later at the Lycée Louis le Grand in Paris. His studies at the école Polytechnique, where he en-rolled in 1815, ended the following year, because that institution was dissolved when its students persisted in their loyalty to the Napoleonic regime. In 1818 Bienaymé became lecturer in mathematics at Saint-Cyr, the French equivalent of West Point. In the end, he joined the civil service as a general inspector of finance.

After Bienaymé became a civil servant, he began his studies of actuarial science, statistics, and prob-ability. Baron Louis, France’s able minister of finance during the Bourbon restoration, was inclined to make use of technical advice, and Bienaymé became closely associated with Louis’s work. Bienaymé’s career in the civil service was not interrupted by the revolution of 1830, but after the revolution of 1848 he retired and devoted all his time to scientific work.

Bienaymé’s retirement made possible his active participation in the affairs of various scientific societies. He became a member of the Société Philomatique (an association for the advancement of science) and, on July 5, 1852, he was elected a member of the Institut de France (Académie des Sciences). At the time of his death, he was a corresponding member of the Science Academy of St. Petersburg and of the Central Commission of Statistics of Belgium, and an honorary member of the Chemical Conference Association of Naples. As a member of the Academie des Sciences he acted for 23 years as a referee for the Montyon Prize, the highest French award for achievement in statistics, and his interesting judgments of the candidates for this distinction can be found in the records of the academy.

Bienaymé published many papers in the proceedings of the academy. Among these is an important one on runs, giving a theorem for the probable number of maxima and minima of a sequence of observed numbers. In 1853 Bienaymé discovered a very important inequality: the probability that the inequality ǀXǀ ≥ tσ is true is less than or equal to 1/t2, X being a random variable with mean zero and standard deviation σ (1853a). The Russian mathematician Chebyshev independently published the same discovery some twelve years later.

Scientific controversies had considerable appeal for Bienaymé. He debated with Cauchy about the relative merits of the least squares method and of an interpolation procedure proposed by the latter (1853b). He also criticized the extension by Poisson of a theorem of Jacques Bernoulli, the so-called law of large numbers (1855). In addition to the criticism of Poisson, this paper contains a keen analysis of meteorological data, especially those having to do with rainfall.

In spite of his retirement, Bienaymé had considerable influence, as a statistical expert, in the government of Napoleon III. In 1864 Napoleon’s minister, Dumas, praised Bienaymé in the French Senate for the help he had given to the administration in connection with the actuarial work required for the creation of a retirement fund.

Daniel DuguÉ

[For the historical context of Bienaymé’s work, see the biographies of theBernoulli family; Poisson. For discussion of the subsequent development of his ideas, seeNonparametric statistics, article onRuns; Probability.]


1837 De la durée de la vie en France depuis le commencement du XIXe siècle. Annales d’hygiéne publique et de médicine légale 18:177−218.

1838a Mémoire sur la probabilité des resultats moyens des observations: Démonstration directe de la règie de Laplace. Académie des Sciencés, Paris, Mémoires présentes par divérs savants; sciences mathématiques et physiques 2d Series 5:513−558.

1838b Probabilité des jugements et des témoinages. Société Philomatique de Paris, Extraits des procèsverbaux des séances 5th Series 3:93−96.

1853a Considérations è I’appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés. Académie des Sciences, Paris, Comptes-rendus hebdomadaires des séances 37:309−324.

1853b Remarques sur les différences qui distinguent I’interpolation de M. Cauchy de la méthode des méindres carrés, et qui assurent la supériorité de cette méthode. Académie des Sciences, Paris, Comptes-rendus hebdomadaires des séances 37:5−13.

1855 Communication sur un principe que M. Poisson avait cru découvrir et qu’il avait appelé loi des grands nombres. Académie des Sciences Morales et Politiques, Séances et travaux 31:379−389.

1875 Application d’un théorème nouveau du calcul des probabilités. Académie des Sciences, Paris, Comptesrendus hebdomadaires des séances 81:417−423.


M. de la Gournerie donne lecture de la note suivante, sur les travaux de M. Bienaymé. 1878 Académic des Sciences, Paris, Comptes-rendus hebdomadaires des séances 87:617−619.

Notice sur les travaux scientifiques de M. I. J. Bienaymé … inspecteur général des finances. 1852 Paris: Bachelier.