## 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.

Original language | English |
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Pages (from-to) | 271-282 |

Number of pages | 12 |

Journal | Applicable Analysis and Discrete Mathematics |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - Oct 2011 |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics