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First-passage times for the partial sums of a sequence of geometric distributions

Published online by Cambridge University Press:  14 July 2016

A. J. Woods
A. J. Woods*
Affiliation:
University of Reading
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Abstract

It is shown here that questions about the probability distributions of the partial sums of a sequence of geometric distributions, all with different parameters, can be answered by considering the transition probabilities of a homogeneous Markov chain. The result is applied to the embedded random walk of an epidemic process.

Keywords

CARRIERS EPIDEMICFIRST-PASSAGE TIMEGEOMETRIC DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 430 - 432
Copyright
Copyright © Applied Probability Trust 1982 

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References

Downton, F. (1967) Epidemics with carriers: a note on a paper of Dietz. J. Appl. Prob. 4, 264–270.CrossRefGoogle Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.CrossRefGoogle ScholarPubMed