A Mixture of Generalized Negative Binomial Distribution with Generalized Exponential Distribution

The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional statistical distributions such as Poisson and negative binomial cannot be used efficiently. In this paper an attempt has been made to obtain a mixture of generalized negative binomial distribution with that of generalized exponential distribution, which is obtained by mixing the generalized negative binomial distribution with generalized exponential distribution. The new mixed distribution so obtained generalizes several distributions that have been discussed in literature. Estimation of the parameters, factorial moment and ordinary moments of the new distribution has also been discussed. To justify the suitability, the distribution is fitted to a reported count data set. The resulting fit is found to be good in comparison to others.