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Exact distribution of kin number in multitype Galton-Watson process

  • A. Joffe
  • W. A. O’N. Waugh

Abstract

For more background on this subject we refer the reader to Waugh (1981), Joffe and Waugh (1982) and (1985). Here we borrow freely from those articles.

Keywords

Exact Distribution Fixed Type Sibling Group Multiple Primary Cancer Familial Cancer Syndrome 
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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References

  1. Adams, K.J. (1981). The role of children in the changing socio-economic strategies of the Guyanese Caribs. Canad.J. Anthropol.Google Scholar
  2. Athreya, K.B. and P. Ney (1972). Branching processes. Springer-Verlag.Google Scholar
  3. Burks, B.S. (1933). A statistical method for estimating the distribution of sizes of completed fraternities in a population represented by a random sampling of individuals. J.Amer.Statist. Assoc. 28, 388–394.CrossRefGoogle Scholar
  4. Gokalp, C. (1979) Le réseau familial. Population 6, 1077–1094.Google Scholar
  5. Goodman, L.A., N. Keyfitz and T.W. Pullum (1974). Family formation and the frequency of various kinship relationships. Theoret. Popn Biol. 5, 1–27.CrossRefGoogle Scholar
  6. Goodman, L.A., N. Keyfitz and T.W. Pullum (1975). Addendum to “Family formation and the frequency of various kinship relationships”. Theoret.Popn Biol. 8, 376–381.CrossRefGoogle Scholar
  7. Jegers, P. (1982). How probable is it to be firstborn? and other branching process applications to kinship problems. Math. Biosci. 59, 1–15.MathSciNetCrossRefGoogle Scholar
  8. Joffe, A. and W.A.O’N. Waugh (1982). Exact distributions of kin numbers in a Galton-Watson process. J.Appl.Prob. 19, 767–775.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Joffe, A. and W.A.O’N.Waugh (1985). The kin number problem in a multitype Galton-Watson process. J.Appl.Prob.Google Scholar
  10. Le Bras, H. (1973). Parents, grands-parents, bisaïeuls. Population 1, 9–38.CrossRefGoogle Scholar
  11. Lynch, H.T., H.D. Guirgis, P.M. Lynch, J.F. Lynch and R.D. Harris (1977a). Familial cancer syndromes, a survey. Cancer, 39, 1867–18881.CrossRefGoogle Scholar
  12. Lynch, H.T., H.D. Guirgis, P.M. Lynch, J.F. Lynch and R.D. Harris (1977b). Rôle of heredity in multiple primary cancer. Cancer 40, 1849–1854.CrossRefGoogle Scholar
  13. McKusick, V.A. (1965). Some computer applications to problems in human genetics. Methods of Information in Medicine IV 4, 183–189.Google Scholar
  14. Morgan, W.K.C. (1979). Industrial carinogens: the extent of the risk. Thorax 34, 431–433.CrossRefGoogle Scholar
  15. Nerman, O. (1984). The growth and composition of supercritical branching populations on general typespaces. Preliminary manuscript, Department of Mathematics, Chalmers University of Technology and the University of Göteborg.Google Scholar
  16. Nerman, O. and P. Jagers (1984). The stable doubly infinite pedigree process of supercritical branching populations. Z.Wahrscheinlichkeitstheorie verw.Gebiete 65, 445–460.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Neveu, J. (1985). Recent results on branching processes. Those proceedings.Google Scholar
  18. Waugh, W.A.O’N. (1981). Application of the Galton-Watson process to the kin number problem. Adv.Appl.Prob. 13, 631–649.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • A. Joffe
    • 1
  • W. A. O’N. Waugh
    • 2
  1. 1.Université de MontréalQuebecCanada
  2. 2.The University of TorontoCanada

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