Filters

2017 - 20183
Reset filters

Settings

Author: Eryilmaz, SerkanSubject: Compound distributions

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On compound sums under dependence
    (Elsevier, 2017) Eryilmaz, Serkan
    In this paper, we study the compound random variable S = Sigma(N)(t-1) Y-t when there is a dependence between a random variable N and a sequence of random variables {Y-t}(t >= 1). Such a compound random variable has been found to be useful in several fields including actuarial science, risk management, and reliability. In particular, we develop some results on distributional properties of the random variable S when N is a phase-type random variable that is defined on a sequence of binary trials and depends on {Y-t}(t >= 1). We "present illustrative examples and an application for the use of results in actuarial science. (C) 2016 Elsevier B.V. All rights reserved.
  • Thumbnail Image
    Article
    Citation - WoS: 7
    Citation - Scopus: 7
    A Generalized Class of Correlated Run Shock Models
    (de Gruyter Poland Sp Zoo, 2018) Yalcin, Femin; Eryilmaz, Serkan; Bozbulut, Ali Riza
    In this paper, a generalized class of run shock models associated with a bivariate sequence {(X-i, Y-i)}(i >= 1) of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X-1, X-2, ... over time, let the random variables Y-1, Y-2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = Sigma(N)(t=1) Y-t, where N is a stopping time for the sequence {Xi}(i >= 1) and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {X-i, 1 <= i <= N}Distributions of T and M are investigated when N has a phase-type distribution.
  • Thumbnail Image
    Article
    Citation - WoS: 14
    Citation - Scopus: 17
    Compound Geometric Distribution of Order k
    (Springer, 2017) Koutras, Markos V.; Eryilmaz, Serkan
    The 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.