Poisson-Gamma Counting Process as a Survival Model under Size-Biased Sampling

In this paper a Size-Biased PoissonGamma distribution (SBPGD) has been proposed, which is obtained by compounding a Size-Biased Poisson distribution with a Size-Biased two parameter Gamma distribution. In this paper the pmf of the proposed distribution (SBPGD) 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.