I.J. Bienayme [1796-1878]: Criticality, inequality, and internationalization

Two striking contributions of Bienayme to mathematical statistics: (1) a co mpletely correct statement of the Criticality Theorem for simple branching processes in 1845; and (2) the derivation of the Bienayme-Chebyshev Inequal ity, are revisited on the 200th anniversary of his birth. We use writings a nd archival materials available since the note of Heyde & Seneta (1972) to present a fuller biographical picture. Bienayme's connections with Buniakov sky and Chebyshev are elucidated, and his role in furthering Chebyshev's in ternational contacts outlined. A concluding section illuminates Bienayme's understanding of the linear regression of one random variable on another in an actuarial context of random shocks.