On a class of hyper-Poisson and alternative hyper-Poisson distributions

Here we propose a class of hyper-Poisson and alternative hyper-Poisson distributions and study some of its important aspects by deriving expressions for its probability mass function, mean and variance and obtain conditions under which the distribution becomes under-dispersed or over-dispersed. Certain recurrence relations for probabilities, raw moments and factorial moments are also developed. Further, the estimation of the parameters of this class of hyper-Poisson distributions is attempted by various methods of estimation and shown that this new class of distribution gives better fit to certain real life data sets compared to the existing models.