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I. J. Bienayme

Our interest in 1. J. Bienayme was kindled by the discovery of his paper of 1845 on simple branching processes as a model for extinction of family names. In this work he announced the key criticality theorem 28 years before it was rediscovered in incomplete form by Galton and Watson (after whom the process was subsequently and erroneously named). Bienayme was not an obscure figure in his time and he achieved a position of some eminence both as a civil servant and as an Academician. However, his is no longer widely known. There has been some recognition of his name work on least squares, and a gradually fading attribution in connection with the (Bienayme-) Chebyshev inequality, but little more. In fact, he made substantial contributions to most of the significant problems of probability and statistics which were of contemporary interest, and interacted with the major figures of the period. We have, over a period of years, collected his traceable scientific work and many interesting features have come to light. The present monograph has resulted from an attempt to describe his work in its historical context. Earlier progress reports have appeared in Heyde and Seneta (1972, to be reprinted in Studies in the History of Probability and Statistics, Volume 2, Griffin, London; 1975; 1976).
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Table of Contents

1. Historical background.- 1.1. Introduction.- 1.2. A historical prelude.- 1.3. Biography.- 1.4. Academic background and contemporaries.- 1.5. Bienayme in the literature.- 1.6. The Societe Philomatique and the journal L'Institut.- 2. Demography and social statistics.- 2.1. Introduction.- 2.2. Infant mortality and birth statistics.- 2.3. Life tables.- 2.4. Probability and the law.- 2.5. Insurance and retirement funds.- 3. Homogeneity and stability of statistical trials.- 3.1. Introduction.- 3.2. Varieties of heterogeneity.- 3.3. Bienayme and Poisson's Law of Large Numbers.- 3.4. Dispersion theory.- 3.5. Bienayme's test.- 4. Linear least squares.- 4.1. Introduction.- 4.2. Legendre, Gauss, and Laplace.- 4.3. Bienayme's contribution.- 4.4. Cauchy's role in interpolation theory.- 4.5. Consequences.- 4.6. Bienayme and Cauchy on probabilistic least squares.- 4.7. Cauchy continues.- 5. Other probability and statistics.- 5.1. Introduction.- 5.2. A Limit theorem in a Bayesian setting.- 5.3. Medical statistics.- 5.4. The Law of Averages.- 5.5. Electoral representation.- 5.6. The concept of sufficiency.- 5.7. A general inequality.- 5.8. A historical note on Pascal.- 5.9. The simple branching process.- 5.10. The Bienayme-Chebyshev Inequality.- 5.11. A test for randomness.- 6. Miscellaneous writings.- 6.1. A perpetual calendar.- 6.2. The alignment of houses.- 6.3. The Montyon Prize reports.- Bienayme's publications.- Name index.

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