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Margaret Archibald - Position of the maximum in a sequence with geometric distribution

dmtcs:3367 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3367
Position of the maximum in a sequence with geometric distributionConference paper

Authors: Margaret Archibald 1

  • 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).


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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