Separation of the maxima in samples of geometric random variables

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dc.contributor.authorBrennan C.
dc.contributor.authorKnopfmacher A.
dc.contributor.authorMansour T.
dc.contributor.authorWagner S.
dc.date.accessioned2012-04-12T08:21:52Z
dc.date.available2012-04-12T08:21:52Z
dc.date.issued2011
dc.description.abstractWe consider samples of n geometric random variables ω 1 ω 2 · · · ω n where ({ω j = i}=pq i-1, for 1 ≤ j ≤ n, with p+q=1. For each fixed integer d > 0, we study the probability that the distance between the consecutive maxima in these samples is at least d. We derive a probability generating function for such samples and from it we obtain an exact formula for the probability as a double sum. Using Rice's method we obtain asymptotic estimates for these probabilities. As a consequence of these results, we determine the average minimum separation of the maxima, in a sample of n geometric random variables with at least two maxima.
dc.identifier.citationApplicable Analysis and Discrete Mathematics
dc.identifier.citation5
dc.identifier.citation2
dc.identifier.citation271
dc.identifier.citation282
dc.identifier.issn14528630
dc.identifier.other10.2298/AADM110817019B
dc.identifier.urihttp://hdl.handle.net/10019.1/20581
dc.subjectAsymptotics
dc.subjectGeometric random variables
dc.subjectMaxima
dc.subjectProbability generating functions
dc.titleSeparation of the maxima in samples of geometric random variables
dc.typeArticle
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