A Bivariate Gamma Mixture Discrete Pareto Distribution
AuthorAmponsah, Charles Kwame
AdvisorKozubowski, Tomasz J.
Mathematics and Statistics
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We study a four-parameter generalization of the of bivariate exponential geometric (BEG) law of Kozubowski and Panorska (2005) and bivariate gamma geometric (BGG) law (Barreto-Souza, 2012). The new bivariate distribution is referred to as gamma mixture discrete Pareto (GMDP) law. A bivariate random vector (X;N) follows GMDP law if N is a two-parameter discrete Pareto random variable studied by Buddana and Kozubowski (2014) and X is the sum of N independent, identically distributed gamma random variables, independent of N. Our results include conditional and marginal distributions, integral transforms, moments and covariance matrix. We also study the problem of parameter estimation using maximum likelihood and simulation studies to validate our estimation strategies, which for the most part do not produce estimators in explicit forms.