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Renewal processes with random numbers of delays: application to a conception and birth model

Published online by Cambridge University Press:  14 July 2016

Kenneth Lange  and
Norman J. Johnson
Kenneth Lange
Affiliation:
University of California, Los Angeles
Norman J. Johnson
Affiliation:
University of California, Los Angeles
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Abstract

Asymptotic formulas and Laplace–Stieltjes transforms are derived for the first two moments of a renewal process with a random number of delays. These are simplified when all the delays follow the same distribution. An asymptotic occupancy result is also derived for two-stage renewal processes with random numbers of delays. As an example, a demographic model of conception and birth is discussed. This model represents the sequence of live births to a woman as a renewal process. If the woman practises birth control after achieving her desired family composition, the renewal process has a random number of delays.

Keywords

RENEWAL THEORYDELAYLAPLACE–STIELTJES TRANSFORMASYMPTOTIC FORMULASCONCEPTION AND BIRTH MODEL
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 209 - 224
Copyright
Copyright © Applied Probability Trust 1978 

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