The distribution of ascents of size $d$ or more in samples of geometric random variables

Charlotte Brennan 1 Arnold Knopfmacher 1
1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]
Abstract : We consider words or strings of characters $a_1a_2a_3 \ldots a_n$ of length $n$, where the letters $a_i \in \mathbb{Z}$ are independently generated with a geometric probability $\mathbb{P} \{ X=k \} = pq^{k-1}$ where $p+q=1$. Let $d$ be a fixed nonnegative integer. We say that we have an ascent of size $d$ or more if $a_{i+1} \geq a_i+d$. We determine the mean, variance and limiting distribution of the number of ascents of size $d$ or more in a random geometrically distributed word.
Keywords : geometric random variables distributions generating functions
Type de document :
Communication dans un congrès
Conrado Martìnez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.343-352, 2005, DMTCS Proceedings
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Charlotte Brennan, Arnold Knopfmacher. The distribution of ascents of size $d$ or more in samples of geometric random variables. Conrado Martìnez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.343-352, 2005, DMTCS Proceedings. 〈hal-01184217〉

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