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Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis
K.K Jose
*
and Shalitha Jacob
Version 1
: Received: 25 August 2016 / Approved: 26 August 2016 / Online: 26 August 2016 (09:43:14 CEST)
How to cite: Jose, K.; Jacob, S. Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis. Preprints 2016, 2016080209 (doi: 10.20944/preprints201608.0209.v1). Jose, K.; Jacob, S. Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis. Preprints 2016, 2016080209 (doi: 10.20944/preprints201608.0209.v1).
Abstract
In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-di fferential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fi xed at zero.
Subject Areas
bivariate generalized power series distribution; ruin probability; aggregate claims distribution
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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