A solution to the distribution problems arising in the studies of a two- sex population process
type: Item
instance of: scholarly article
title: A solution to the distribution problems arising in the studies of a two- sex population process
zbMATH Open document ID: 0569.92017
DOI: 10.1016/0304-4149(85)90036-5
author: P. K. Tapaswi
author: R. Roychoudhury
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors analyse a model of population growth involving two sexes in which the birth rates of both males and females depend only on the female population size. Using the Markov property of the process, the authors set up a partial differential equation for the probability generating function of the sizes of the two sexes. The resulting partial differential equation is then solved and an explicit formula for the covariance of the sizes of the male and female population is provided. The authors apparently do not seem to be aware of the usefulness of the backward equation technique [see \textit{M. S. Bartlett}, An introduction to stochastic processes (1955; Zbl 0068.118), p. 42] which would have resulted in considerable simplicity and calculational ease, particularly when higher order moments and correlations are needed.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 3910201
zbMATH Keywords: two-sex population process
zbMATH Keywords: marriage dominance
zbMATH Keywords: marginal distribution
zbMATH Keywords: Riccati equation
zbMATH Keywords: confluent hypergeometric function
zbMATH Keywords: model of population growth
zbMATH Keywords: partial differential equation
zbMATH Keywords: probability generating function
zbMATH Keywords: covariance
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90036-5
OpenAlex ID: W2002953383
cites work: Q5544744
cites work: Q3273545
cites work: Immigration in the two-sex population process
cites work: Q5831527
cites work: Q3272638
cites work: Q4048871
cites work: Q3259158
description: scientific article; zbMATH DE number 3910201