Discrete Mathematics & Theoretical Computer Science |

- 1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]

As a sequel to [arch04], the position of the maximum in a geometrically distributed sample is investigated. Samples of length n are considered, where the maximum is required to be in the first d positions. The probability that the maximum occurs in the first $d$ positions is sought for $d$ dependent on n (as opposed to d fixed in [arch04]). Two scenarios are discussed. The first is when $d=αn$ for $0 < α ≤ 1$, where Mellin transforms are used to obtain the asymptotic results. The second is when $1 ≤ d = o(n)$.

Source: HAL:hal-01184039v1

Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms

Section: Proceedings

Published on: January 1, 2005

Imported on: May 10, 2017

Keywords: Mellin transforms,generating functions,geometric distribution.,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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