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Random displacements of regularly spaced events

Published online by Cambridge University Press:  14 July 2016

Roger B. Nelsen  and
Trevor Williams
Roger B. Nelsen
Affiliation:
Lewis and Clark College, Portland, Oregon
Trevor Williams
Affiliation:
University of Bristol
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Abstract

We consider the point process i + τi (i = 0, ± 1, ± 2, . . .), where the τi(assumed for convenience to be positive) are independent random samples from the same distribution. We define an inter-arrival interval as the stretch between neighbouring events, which need not belong to successive values of i, because of the jumbling of position occasioned by the variability of the τ. We obtain explicit expressions for the distribution of inter-arrival intervals in general, as well as the correlation coefficient between successive inter-arrival intervals in the case where the τ are exponentially distributed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 183 - 195
Copyright
Copyright © Applied Probability Trust 

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