Poisson-Gamma Counting Process as a Discrete Survival Model

In this paper a PoissonGamma distribution has been proposed, which is obtained by compounding a Poisson distribution with a two parameter Gamma distribution. Here the pmf of the proposed distribution (PGD) is derived. The expressions for raw moments, central moments, coefficients of skewness and kurtosis have been derived. Survival and Hazard functions of proposed distribution are also obtained. The estimator of the parameters have been obtained by method of Moments as well as method of Maximum Likelihood. The proposed distribution has found to be a good fit of Kemp & Kemp survival data (1965).