Compound Markov negative binomial distribution
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Date
2016
Authors
Eryilmaz, Serkan
Eryılmaz, Serkan
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Publisher
Elsevier
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Abstract
Let {Y-i}(i >= 1) be a sequence of {0,1} variables which forms a Markov chain with a given initial probability distribution and one-step transition probability matrix. Define N-n to be the number of trials until the nth success ("1") in {Y-i}(i >= 1). In this paper, we study the distribution of the random variable T = Sigma(Nn)(i=1) X-i, where {X-i}(i >= 1) is a sequence of independent and identically distributed random variables having a common phase-type distribution. The distribution of T is obtained by means of phase-type distributions. (C) 2015 Elsevier B.V. All rights reserved.
Description
Eryilmaz, Serkan/0000-0002-2108-1781
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Keywords
Compound random variable, Markov chain, Phase-type distribution
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Citation
10
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Q1
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Source
Volume
292
Issue
Start Page
1
End Page
6