On the Partial-Geometric Distribution: Properties and Applications

In this article we introduce the new, two-parameter partial-geometric distribution (PG) that contains both geometric and first success distributions as a particular case. Some probability and statistical properties of the proposed distribution are discussed, including probability mass function, mean, variance, moment generating function, and probability generating function. We propose the method of maximum likelihood for estimating the model’s parameters, and apply the PG distribution to two real datasets to illustrate the flexibility of the proposed distribution. We found the PG distribution is more dynamic than the geometric distribution in the sense that it can be applied to the under-dispersed data. The PG distribution also performs well with a goodness of fit test and some other model selection characteristics for model fitting of these two datasets. Thus, the PG distribution can be applied as an alternative model for the analysis of discrete data.