Tank, FatihEryilmaz, SerkanIndustrial Engineering2024-07-052024-07-0520150932-50261613-979810.1007/s00362-014-0632-42-s2.0-84945305097https://doi.org/10.1007/s00362-014-0632-4https://hdl.handle.net/20.500.14411/791tank, fatih/0000-0003-3758-396X; Tank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781Geometric 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.eninfo:eu-repo/semantics/closedAccessGeometric distribution of order kPhase-type distributionReliabilityThe Distributions of Sum, Minima and Maxima of Generalized Geometric Random VariablesArticleQ356411911203WOS:00036412630001623