Eryilmaz, SerkanEryılmaz, SerkanIndustrial Engineering2024-07-052024-07-052016100377-04271879-177810.1016/j.cam.2015.06.0262-s2.0-84937019632https://doi.org/10.1016/j.cam.2015.06.026https://hdl.handle.net/20.500.14411/490Eryilmaz, Serkan/0000-0002-2108-1781Let {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.eninfo:eu-repo/semantics/openAccessCompound random variableMarkov chainPhase-type distributionArticleQ129216WOS:000362130400001