Inhomogeneous birth-death and birth-death-immigration processes and the logarithmic series distribution. Part 2

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:86

Article

Branson, D

关键词: inhomogeneous birth-death process;    inhomogeneous birth-death-immigration process;    logarithmic series distribution;   

DOI  :  10.1016/S0304-4149(99)00093-9

来源: Elsevier

【 摘 要 】

A simple graphical argument described in a previous paper is used to show that the zero-modified geometric form of the population-size distribution of a time-inhomogeneous birth-and-death model is maintained when the death rates of individuals depend on their ages and times of birth. An explicit form for the population-size distribution is found. Certain models incorporating immigration, but again with general lifetime distributions, continue to lead to Fisher's logarithmic series distribution for the abundance of families of a particular size. It is shown that the zero-modified geometric form no longer holds if the model is extended to incorporate age-dependent birth rates. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free