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Bienaymé, Cournot and the extinction of family names (1845–1847)

  • Nicolas Bacaër

Abstract

The French statistician Bienaymé understood in 1845 how to compute the probability of a family name becoming extinct if each male has a number of sons following a given probability distribution. If the average number of sons is less than or equal to one, the family name will become extinct. It the average is bigger than one, the extinction probability is strictly less than one. The proof of his result was published two years later in a book written by his friend Cournot. These works were rediscovered only recently.

Keywords

Vote System Male Offspring Extinction Probability Family Line General Inspector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Further reading

  1. 1.
    Bienaymé, I.J.: De la loi de multiplication et de la durée des familles. Soc. Philomat. Paris 5, 37–39 (1845) Reprinted in Kendall (1975) Google Scholar
  2. 2.
    Bru, B.: À la recherche de la démonstration perdue de Bienaymé. Math. Sci. Hum. 114, 5–17 (1991). archive.numdam.org MATHMathSciNetGoogle Scholar
  3. 3.
    Bru, B., Jongmans, F., Seneta, E.: I.J. Bienaymé: Family information and proof of the criticality theorem. Int. Stat. Rev. 60, 177–183 (1992) MATHCrossRefGoogle Scholar
  4. 4.
    Cournot, A.-A.: De l’origine et des limites de la correspondance entre l’algèbre et la géométrie. Hachette, Paris (1847). books.google.com Google Scholar
  5. 5.
    Doubleday, T.: The True Law of Population. Simpkin, Marshall, & Co., London (1842). www.archive.org Google Scholar
  6. 6.
    Heyde, C.C., Seneta, E.: I.J. Bienaymé: Statistical Theory Anticipated. Springer-Verlag, New York (1977) Google Scholar
  7. 7.
    Kendall, D.G.: The genealogy of genealogy: branching processes before (and after) 1873. Bull. Lond. Math. Soc. 7, 225–253 (1975) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Littré, É.: Conservation, révolution et positivisme. Ladrange, Paris (1852). books.google.com Google Scholar
  9. 9.
    Malthus, T.R.: An Essay on the Principle of Population, 2nd edn. Bensley, London (1803). www.archive.org Google Scholar
  10. 10.
    Martin, T.: Antoine Augustin Cournot. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 152–156. Springer, New York (2001) Google Scholar
  11. 11.
    Seneta, E.: Irenée-Jules Bienaymé. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 132–136. Springer, New York (2001) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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