The distributions of sum, minima and maxima of generalized geometric random variables

Fatih Tank () and Serkan Eryilmaz ()

Statistical Papers, 2015, vol. 56, issue 4, 1203 pages

Abstract: Geometric distribution of order $$k$$ k as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first $$k$$ k consecutive successes in Bernoulli trials with success probability $$p$$ p . 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 $$k$$ k are obtained. Numerical results are presented to illustrate the computational details. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Geometric distribution of order $$k$$ k; Phase-type distribution; Reliability; 60E05; 62E15 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s00362-014-0632-4

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