Koutras, Markos V.Eryilmaz, SerkanIndustrial Engineering2024-07-052024-07-0520171387-58411573-771310.1007/s11009-016-9482-y2-s2.0-84957539194https://doi.org/10.1007/s11009-016-9482-yhttps://hdl.handle.net/20.500.14411/2868Koutras, Markos/0000-0001-5160-2405; Eryilmaz, Serkan/0000-0002-2108-1781The distribution of the number of trials until the first k consecutive successes in a sequence of Bernoulli trials with success probability p is known as geometric distribution of order k. Let T (k) be a random variable that follows a geometric distribution of order k, and Y (1),Y (2),aEuro broken vertical bar a sequence of independent and identically distributed discrete random variables which are independent of T (k) . In the present article we develop some results on the distribution of the compound random variable Y-t.eninfo:eu-repo/semantics/closedAccessCompound distributionsGeometric distribution of order kPhase-type distributionRunsArticleQ4Q3192377393WOS:00040143280000213