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The spectrum of intervals of a geometric branching poisson process

Published online by Cambridge University Press:  14 July 2016

D. C. Gilles  and
P. A. W. Lewis
D. C. Gilles
Affiliation:
Computing Laboratory, University of Glasgow
P. A. W. Lewis
Affiliation:
IBM Research Laboratory, Yorktown Heights, New York
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Abstract

A summation formula is given for computing the spectrum of intervals of a geometric branching Poisson process from the cumulant generating function of the associated counting process.

Type
Short Communications
Information
Journal of Applied Probability , Volume 4 , Issue 1 , November 1967 , pp. 201 - 205
Copyright
Copyright © Applied Probability Trust 

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References

[1] Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London, and Wiley, New York.Google Scholar
[2] Lewis, P. A. W. (1964a) A branching Poisson process model from the analysis of computer failure patterns. J. R. Statist. Soc. B 26, 398–456.Google Scholar
[3] Lewis, P. A. W. (1964b) The implications of a failure model for the use and maintenance of computers. J. Appl. Prob. 1, 347–368.Google Scholar
[4] Lewis, T. (1961) The intervals between regular events displaced in time by independent random deviations of large dispersion. J. R. Statist. Soc. B 23, 476–483.Google Scholar