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A note on the two-sex population process

Published online by Cambridge University Press:  14 July 2016

J. Gani  and
Pyke Tin
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Abstract

This paper considers the two-sex birth-death model {X(t), Y(t); t ≧ 0}; an explicit solution is obtained for its probability generating function. It is shown that moments of the process can be found directly from the Kolmogorov forward equations for the probabilities. An integral equation approach is also used to throw light on the structure of the process.

Keywords

BIRTH-DEATH PROCESSRICCATI EQUATIONINTEGRAL EQUATION APPROACH
Type
Part 6—Allied Stochastic Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 335 - 344
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. Dover Publications, New York.Google Scholar
Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219–230.CrossRefGoogle Scholar
Goodman, L. A. (1953) Population growth of the sexes. Biometrics 9, 212–225.CrossRefGoogle Scholar
Joshi, D. D. (1954) Les processus stochastiques en démographie. Publ. Inst. Statist. Univ. Paris 3, 153–177.Google Scholar
Srinivasan, S. K. and Ranganathan, C. R. (1983) Parity dependent population growth models. J. Math. Phys. Sci. 17, 279–292.Google Scholar
Tapaswi, P. K. and Roychoudhury, R. K. (1983) A new approach to the distribution problems arising in the studies of population growth of sexes. Technical Report, 151 Calcutta.Google Scholar
Tapaswi, P. K. and Roychoudhury, R. K. (1985) A solution to the distribution problems arising in the studies of a two-sex population process. Stoch. Proc. Appl. 19, 359–370.CrossRefGoogle Scholar