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A limit theorem for inter-record times

Published online by Cambridge University Press:  14 July 2016

R. W. Shorrock
R. W. Shorrock*
Affiliation:
The University of British Columbia, Vancouver
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Abstract

A limit theorem for inter-record times is obtained which seems to explain many of their known asymptotic properties. The process of inter-record times is shown to be approximately non-homogeneous Poisson.

Keywords

POISSON PROCESSINTER-RECORD TIMESRECORD VALUESGEOMETRIC LAW
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 219 - 223
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Brown, M. (1969) An invariance property of Poisson processes. J. Appl. Prob. 6, 453–458.Google Scholar
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[4] Shorrock, R. W. (1970) Caravans in traffic flow. Stanford University Technical Report No. 20.Google Scholar
[5] Strawderman, W. and Holmes, P. T. (1970) On the law of the iterated logarithm for inter-record times. J. Appl. Prob. 7, 432–439.Google Scholar
[6] Tata, M. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.Google Scholar