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
NULL##NULL
Charlotte Brennan;Arnold Knopfmacher
1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]
We consider words or strings of characters a1a2a3…an of length n, where the letters ai∈Z are independently generated with a geometric probability P{X=k}=pqk−1 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+1≥ai+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.