A Bivariate Distribution Connected with Poissonian Maxima of Exponential Variables
AdvisorKozubowski, Tomasz J.
Mathematics and Statistics
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In this work we present a bivariate distribution of X and N, where N has a Poisson distribution and X is the maximum of N independent, identically distributed exponential variables. The joint bivariate distribution is developed, along with some useful representations of the model. The results also include univariate marginal and conditional distributions, moments and the covariance matrix, simulation, and estimation of the parameters.