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Two-sex Branching Models with Random Control on the Number of Progenitor Couples

Author

Listed:
  • Manuel Molina

    (University of Extremadura)

  • Manuel Mota

    (University of Extremadura)

  • Alfonso Ramos

    (University of Extremadura)

Abstract

In this paper we introduce a class of two-sex branching models where, in each generation, a random control on the number of progenitor couples in the population is considered. For such a class, several probabilistic results are established. Also assuming offspring probability distribution belonging to the bivariate power series family, Bayes estimators for the mean vector and the covariance matrix of the offspring distribution are proposed. A computational method to determine highest posterior density credibility sets is stated. As illustration, a simulated example is provided.

Suggested Citation

  • Manuel Molina & Manuel Mota & Alfonso Ramos, 2012. "Two-sex Branching Models with Random Control on the Number of Progenitor Couples," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 35-48, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9167-x
    DOI: 10.1007/s11009-010-9167-x
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    References listed on IDEAS

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    1. González, M. & Molina, M. & Mota, M., 2000. "Limit behaviour for a subcritical bisexual Galton-Watson branching process with immigration," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 19-24, August.
    2. Molina, Manuel & del Puerto, Inés M. & Ramos, Alfonso, 2007. "A class of controlled bisexual branching processes with mating depending on the number of progenitor couples," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1737-1743, December.
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    Cited by:

    1. Cristina Gutiérrez & Carmen Minuesa, 2020. "A Predator–Prey Two-Sex Branching Process," Mathematics, MDPI, vol. 8(9), pages 1-26, August.

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    1. Molina, Manuel & del Puerto, Inés M. & Ramos, Alfonso, 2007. "A class of controlled bisexual branching processes with mating depending on the number of progenitor couples," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1737-1743, December.
    2. Shixia Ma & Manuel Molina & Yongsheng Xing, 2012. "Two-Sex Branching Populations With Progenitor Couples in a Random Environment," Mathematical Population Studies, Taylor & Francis Journals, vol. 19(4), pages 177-187, October.

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