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


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.


Vote System Male Offspring Extinction Probability Family Line General Inspector 
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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). 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). Google Scholar
  5. 5.
    Doubleday, T.: The True Law of Population. Simpkin, Marshall, & Co., London (1842). 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). Google Scholar
  9. 9.
    Malthus, T.R.: An Essay on the Principle of Population, 2nd edn. Bensley, London (1803). 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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