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.
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Further reading
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
Erlang, A.K.: Opgave Nr. 15. Mat. Tidsskr. B, 36 (1929) Translation in Guttorp (1995)
Guttorp, P.: Three papers on the history of branching processes. Int. Stat. Rev. 63, 233–245 (1995). www.stat.washington.edu
Heyde, C.C.: Agner Krarup Erlang. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 328–330. Springer, New York (2001)
Ogborn, M.E.: Johan Frederik Steffensen, 1873–1961. J. R. Stat. Soc. Ser. A 125, 672–673 (1962)
Steffensen, J.F.: Om Sandssynligheden for at Afkommet uddør. Mat. Tidsskr. B, 19–23 (1930) English translation in Guttorp (1995)
Steffensen, J.F.: Deux problèmes du calcul des probabilités. Ann. Inst. Henri Poincaré 3, 319–344 (1933). archive.numdam.org
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Bacaër, N. (2011). Erlang and Steffensen on the extinction problem (1929–1933). In: A Short History of Mathematical Population Dynamics. Springer, London. https://doi.org/10.1007/978-0-85729-115-8_18
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DOI: https://doi.org/10.1007/978-0-85729-115-8_18
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