Random displacements of regularly spaced events
- 1 April 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (01) , 183-195
- https://doi.org/10.1017/s0021900200027042
Abstract
We consider the point process i + τ i (i = 0, ± 1, ± 2, . . .), where the τ i (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.Keywords
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