A Flexible Semi-Poisson Distribution with Applications to Insurance Claims and Biological Data

In this paper, a discrete one-parameter distribution called the semi-Poisson is introduced, which based on set of non-negative integers. It seen that captures over-dispersion and zero-inflation scenarios well. A few properties proposed distribution, such as moments, probability-generating function, index dispersion, recurrence relation for negative moments are presented. The applied to two real-life datasets related insurance claims parasite counts, where it noted perform better than many existing distributions Z+, including some recently introduced ones.