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I.J. Bienaymé [1796–1878]: Criticality, Inequality, and Internationalization *
Author(s) -
Seneta E.
Publication year - 1998
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.1998.tb00374.x
Subject(s) - chebyshev filter , criticality , context (archaeology) , simple (philosophy) , mathematics , inequality , random variable , econometrics , internationalization , multidimensional chebyshev's inequality , mathematical economics , calculus (dental) , epistemology , statistics , economics , linear inequality , philosophy , mathematical analysis , history , physics , rearrangement inequality , archaeology , medicine , dentistry , nuclear physics , microeconomics
Summary 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.