A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros

Abstract

Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley distributions are special cases. Several statistical properties of the proposed distribution are presented. The dispersion index for the proposed distribution is derived and based on the index, it is clear that the proposed distribution can adequately fit the data with properties of overdispersion or underdispersion depending on the choice of the parameters. The proposed distribution is fitted to three overdispersed datasets with large proportion of zeros. The best fitted model is selected based on the values of AIC, mean absolute error and root mean squared error. From the model fittings, it can be concluded that the proposed distribution outperforms Poisson and negative binomial distributions in fitting the count data with overdispersion and large number of zeros.