A New Mixed Poisson Distribution: Modeling and Applications

In this article, a new mixed Poisson distribution that includes the geometric and negative binomial distributions as special cases is proposed. This distribution is obtained by mixing the Poisson distribution with the binomial exponential 2 distribution. The new distribution is overdispersed (i.e., the variance is greater than the mean), and hence, this distribution is able to incorporate the overdispersion that typically occurs in count data sets. Shape and moments properties of the proposed distribution are discussed. Estimation of the model parameters is considered using the method of moments and maximum likelihood approach. We propose an algorithm for generating random data from the new distribution. Three real data applications are also presented to see that new distribution is useful for modeling count data.