Separation of the maxima in samples of geometric random variables

Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour, Stephan Wagner

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)271-282
Number of pages12
JournalApplicable Analysis and Discrete Mathematics
Issue number2
StatePublished - Oct 2011


  • Asymptotics
  • Geometric random variables
  • Maxima
  • Probability generating functions

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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