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The distribution of ascents of size $d$ or more in samples of geometric random variables
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.
Cited literature [6 references]
https://hal.inria.fr/hal-01184217
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 13, 2015 - 1:34:49 PM
Last modification on : Wednesday, February 20, 2019 - 4:32:10 PM
Long-term archiving on: : Saturday, November 14, 2015 - 10:23:31 AM
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 13, 2015 - 1:34:49 PM
Last modification on : Wednesday, February 20, 2019 - 4:32:10 PM
Long-term archiving on: : Saturday, November 14, 2015 - 10:23:31 AM
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