Bivariate Compound Distribution Based on Poisson Maxima of Gamma Variates and Related Applications

In this paper we introduce a new bivariate model called bivariate compound Poisson-gamma model. The corresponding variable of this model are based on compounding the Poisson number of occurrences and maximum of independent identically distributed gamma variates. For this proposed model, several distributional properties have been established. We implement the EM algorithm based on the missing value principle to find the maximum likelihood estimators. Moreover, we use the observed Fisher information matrix to construct approximate confidence intervals. The performance of the EM type algorithm is illustrated via numerical simulation studies. Finally, a natural environment data have been analyzed to see how the proposed model and the respective methods work in practice.