Inhomogeneous birth-death and birth-death-immigration processes and the logarithmic series distribution

David Branson

Stochastic Processes and their Applications, 1991, vol. 39, issue 1, 131-137

Abstract: The modified geometric distribution for the population size of a time-inhomogeneous linear birth-and-death model is obtained by a simple graphical argument. A time-inhomogeneous birth-death-immigration process with a particular relationship between birth and immigration rates is shown to lead to Fisher's logarithmic series distribution for the abundance of families of a particular size (and hence to, for example, Ewens' formula for the allelic distribution of a population).

Keywords: inhomogeneous; birth-death; process; inhomogeneous; birth-death-immigration; process; logarithmic; series; distribution (search for similar items in EconPapers)
Date: 1991
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