The Negative Binomial-Sushila Distribution with Application in Count Data Analysis

In this paper, we introduce a negative binomial-Sushila distribution which is a new mixed negative binomial distribution. The probability mass function (pmf) has been expressed as mixtures of the negative binomial and the Sushila distribution. The factorial moments, the first four moments, variance and skewness have been derived. Moreover, we found that the negative binomial-Lindley distribution is its special case. We also discuss maximum likelihood estimation of the model parameters. For application to real data set, it shows that the new distribution can provide a better fit the data than the Poisson and negative binomial distributions. We hope that this distribution may be an alternative model to over-dispersed count data analysis.