In this paper a three parameter generalized alternative hyper-Poisson (GAHP) distribution is defined and discussed. The GAHP distribution contains, as special sub models, several important discrete distributions such as alternative hyper-Poisson (AHP) distribution derived by Kumar and Nair (2012) and Poisson distribution. We develop here the stuttering generalized alternative hyper-Poisson (SGAHP) distribution and discuss some important properties of SGAHP distributions. We also develop the

more »

... ay-Maxwell generalized alternative hyper-Poisson (CMGAHP) distribution in the form of H-power series function and find some of its important properties. Finally, a real data application of CMGAHP distribution is also provided. KEY WORDS Generalized alternative hyper-Poisson distribution, Stuttering generalized alternative hyper-Poisson distribution, Alternative hyper-Poisson distribution, Conway-Maxwell generalized alternative hyper-Poisson distribution, Poisson distribution.