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

David Branson

Stochastic Processes and their Applications, 2000, vol. 86, issue 2, 183-191

Abstract: 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.

Keywords: Inhomogeneous; birth-death; process; Inhomogeneous; birth-death-immigration; process; Logarithmic; series; distribution (search for similar items in EconPapers)
Date: 2000
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