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Erlang and Steffensen on the extinction problem (1929–1933)

  • Nicolas Bacaër

Abstract

In 1929 the Danish telephone engineer Erlang considered once again the problem of extinction of family names. His compatriot statistician Steffensen worked out a complete solution of the problem. He showed in particular that the expectation of the number of offspring in each generation grows exponentially, thus making the bridge between stochastic and deterministic population models.

Keywords

Closed Interval Deterministic Model Extinction Probability Consultative Committee Chief Engineer 
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.
    Brockmeyer, E., Halstrøm, H.L., Jensen, A.: The life and works of A.K. Erlang. Trans. Dan. Acad. Techn. Sci. 2 (1948). oldwww.com.dtu.dk
  2. 2.
    Erlang, A.K.: Opgave Nr. 15. Mat. Tidsskr. B, 36 (1929) Translation in Guttorp (1995) Google Scholar
  3. 3.
    Guttorp, P.: Three papers on the history of branching processes. Int. Stat. Rev. 63, 233–245 (1995). www.stat.washington.edu MATHGoogle Scholar
  4. 4.
    Heyde, C.C.: Agner Krarup Erlang. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 328–330. Springer, New York (2001) Google Scholar
  5. 5.
    Ogborn, M.E.: Johan Frederik Steffensen, 1873–1961. J. R. Stat. Soc. Ser. A 125, 672–673 (1962) Google Scholar
  6. 6.
    Steffensen, J.F.: Om Sandssynligheden for at Afkommet uddør. Mat. Tidsskr. B, 19–23 (1930) English translation in Guttorp (1995) Google Scholar
  7. 7.
    Steffensen, J.F.: Deux problèmes du calcul des probabilités. Ann. Inst. Henri Poincaré 3, 319–344 (1933). archive.numdam.org MATHMathSciNetGoogle 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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