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Preservation of some life length classes for age distributions associated with age-dependent branching processes

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  • Johnson, Richard A.
  • Taylor, James R.

Abstract

Under a Bellman-Harris age-dependent branching process, a parent lives a random length of time and at death produces a random number of offspring. The parent lifetimes have the common cumulative distribution G([dot operator]) and the number of offspring per parent has a common probability distribution. The current age distribution is known to converge to a limiting distribution A([dot operator]), called the Lotka limit law, which depends only on G([dot operator]) and the mean number of offspring. Besides the age distribution, we also consider a residual life distribution and a total life distribution. We investigate the preservation of classes of life lengths for these distributions and their limits.

Suggested Citation

  • Johnson, Richard A. & Taylor, James R., 2008. "Preservation of some life length classes for age distributions associated with age-dependent branching processes," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2981-2987, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2981-2987
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    1. Johnson, Richard A. & Susarla, V. & van Ryzin, John, 1979. "Bayesian non-parametric estimation for age-dependent branching processes," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 307-318, December.
    2. Taylor, James R., 1982. "Backward and forward recurrence times, and their interrelationships in Bellman-Harris branching processes," Statistics & Probability Letters, Elsevier, vol. 1(1), pages 12-16, July.
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    Cited by:

    1. Giada Adelfio & Marcello Chiodi, 2021. "Including covariates in a space-time point process with application to seismicity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 947-971, September.

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