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I.J. Bienaymé [1796–1878]: Criticality, Inequality, and Internationalization

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  • E. Seneta

Abstract

Two striking contributions of Bienaymé to mathematical statistics: (1) a completely correct statemet of the Criticality Theorem for simple branching processes in 1845; and (2) the derivation of the Bienaymé‐Chebyshev Inequality, are revisited on the 200th anniversary of his birth. We use writings and archival materials available since the note of Heyde & Seneta (1972) to present a fuller biographical picture. Bienaymé's connections with Buniakovsky and Chebyshev are elucidated, and this role in furthering Chebyshev's international contacts outlined. A concluding section illuminates Bienaymé's understanding of the linear regression of one random variable on another in an actuarial context of random shocks. L'année 1996 a marqué le deux centiéme anniversaire de la naissance du statisticien Francais Irenée Jules Bienaymé (IJB). Nous poton á nouveau notre attention sur les conributions remarquables, decrites iniialement par Heyde et Seneta (1972). En Particulier, l'aiére‐plan de l'inégalité‐Chebyshev éclaircit la francophilie de Chebyshev, et le role de IJB dans le developpement de la réputation internationale de Chebyshev.

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  • E. Seneta, 1998. "I.J. Bienaymé [1796–1878]: Criticality, Inequality, and Internationalization," International Statistical Review, International Statistical Institute, vol. 66(3), pages 291-301, December.
    • Handle: RePEc:bla:istatr:v:66:y:1998:i:3:p:291-301
    DOI: 10.1111/j.1751-5823.1998.tb00374.x
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