Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2521

 Title: On the Poisson Process of Order k Space Authors: Kostadinova, Krasimira Y. Keywords: Distributions of order kcompound distributionsPoisson processruin probability Issue Date: 2013 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Pliska Studia Mathematica Bulgarica, Vol. 22, No 1, (2013), 117p-128p Abstract: In this notes, the Poisson process of order k as a compound Poisson process is analyzed. We give a brief review of the distributions of order k. Then, some properties of the Poisson process of order k are given as well as probability mass function and recursion formulas. We then describe the defined process as a compound birth process. As application we consider the standard risk model which counting process is the Poisson process of order k. For the Poisson of order k risk model we derive the joint distribution of the time to ruin and the deficit at ruin. As a limiting case we obtain an equation for the ruin probability. We discuss in detail the particular case of exponentially distributed claims. Description: 2010 Mathematics Subject Classification: 60E05, 62P05. URI: http://hdl.handle.net/10525/2521 ISSN: 0204-9805 Appears in Collections: 2013 Volume 22

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