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ON PROBABILITIES ASSOCIATED WITH THE MINIMUM DISTANCE BETWEEN EVENTS OF A POISSON PROCESS IN A FINITE INTERVAL

Published online by Cambridge University Press:  23 April 2010

Shai Covo
Shai Covo
Affiliation:
Department of Mathematics, Bar Ilan University, 52900 Ramat-Gan, IsraelE-mail: green355@netvision.net.il
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Abstract

We revisit the probability that any two consecutive events in a Poisson process N on [0, t] are separated by a time interval that is greater than s (<t) (a particular scan statistic probability) and the closely related probability (recently introduced by Todinov [8], who denotes it as pMFFOP) that before any event of N in [0, t], there exists an event-free interval greater than s. Both probabilities admit simple explicit expressions, which, however, become intractable for very large values of t/s. Our main objective is to demonstrate that these probabilities can be approximated extremely well for large values of t/s by some very tractable and attractive expressions (actually, already for t larger than a few multiples of s).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 3 , July 2010 , pp. 423 - 439
Copyright
Copyright © Cambridge University Press 2010

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