Journal
STATISTICAL PAPERS
Volume 56, Issue 4, Pages 1191-1203Publisher
SPRINGER
DOI: 10.1007/s00362-014-0632-4
Keywords
Geometric distribution of order k; Phase-type distribution; Reliability
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Geometric distribution of order as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first consecutive successes in Bernoulli trials with success probability . In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of order are obtained. Numerical results are presented to illustrate the computational details.
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