Arjun K. Rathie, Pushpa N. Rathie and Paulo H. D. Silva
Explicit expressions of probability functions and probability generating functions for mixed Poisson distributed discrete random variables are given corresponding to the following structure density functions: generalized gamma, generalized shifted gamma and generalized shifted beta. A discrete symmetric distribution corresponding to a stochastic process is approximated by a beta distribution in a more accurate manner. A generalized Beta-Poisson distribution is obtained. The results are useful in biological and economical problems. Special cases are also mentioned. Graphs are drawn for probability functions showing the modality for different values of the parameters. Transition intensities can be easily obtained for the various cases discussed in this paper. Finally, by utilizing the fact that probabilities sum to 1, we obtain some new results for generalized hypergeometric functions.