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Title: On the Poisson Process of Order k Space
Authors: Kostadinova, Krasimira Y.
Keywords: Distributions of order k
compound distributions
Poisson process
ruin 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.
ISSN: 0204-9805
Appears in Collections:2013 Volume 22

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