Negative Binomial-three Parameter Lindley Distribution and ITS Properties

Abstract

In this study, we introduce a mixed distribution by mixing the distributions of negative binomial and three Parameter Lindley distribution This new mixed distribution has a thick tail and may be considered as an alternative for modelling count data with overdispersion. The properties and special cases of the compound distribution are studied. In addition, the parameter estimation for the compound distribution via the method of moments (MME) and the Maximum Likelihood Estimation (MLE) are provided. We present the performance of the Poisson, NB, L3,NBL, NBL2 and NBL3 distribution using real data in terms of log-likelihood, p-value, AIC (Akaike Information Criteria), BIC(Bayesian Information Criteria) and Kolmogorov-Smirnov statistic. It is shown that the negative binomial three parameter Lindley distribution provides a better fit compared to the other distributions under study for fitting over dispersed count data.