Separation of the maxima in samples of geometric random variables
Date
2011
Authors
Brennan C.
Knopfmacher A.
Mansour T.
Wagner S.
Journal Title
Journal ISSN
Volume Title
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Abstract
We 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.
Description
Keywords
Asymptotics, Geometric random variables, Maxima, Probability generating functions
Citation
Applicable Analysis and Discrete Mathematics
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