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Charlotte Brennan ; Arnold Knopfmacher - The distribution of ascents of size d or more in samples of geometric random variables

dmtcs:3382 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3382
The distribution of ascents of size d or more in samples of geometric random variablesConference paper

Authors: Charlotte Brennan 1; Arnold Knopfmacher 1

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

We consider words or strings of characters a1a2a3an of length n, where the letters aiZ are independently generated with a geometric probability P{X=k}=pqk1 where p+q=1. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more if ai+1ai+d. We determine the mean, variance and limiting distribution of the number of ascents of size d or more in a random geometrically distributed word.


Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: geometric random variables,distributions,generating functions,[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]

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