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Simple approximations to the expected waiting time for a cluster of any given size, for point processes

Published online by Cambridge University Press:  01 July 2016

Ester Samuel-Cahn
Ester Samuel-Cahn*
Affiliation:
Hebrew University
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Jerusalem, Israel.
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Abstract

For point processes, such that the interarrival times of points are independently and identically distributed, let T(L, m) denote the time until at least points cluster within an interval of length at most L. Let τ (L, m) + 1 be the total number of points observed until the above happens. Simple approximations of Eτ (L, m) and ET(L, m) are derived, as well as lower and upper bounds for their value. Approximations to the variances are also given. In particular the Poisson, Bernoulli and compound Poisson processes are discussed in detail. Some numerical tables are included.

Keywords

SCANNINGSTOCHASTIC PROCESSINDEPENDENT INTERARRIVAL TIMES: BERNOULLI PROCESS: POISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 21 - 38
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This research was done while the author spent a sabbatical year at Columbia and Rutgers Universities.

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