A New Mixture Distribution for Extreme Excess Zeros: Negative Binomial-Generalized Exponential (NB-GE) Distribution

Abstract

Negative Binomial-Generalized Exponential (NB-GE) distribution is a distribution that capable for modeling overdispersion data with extreme excess zeros, which is more than 80% zeros in a data. The distribution is a mixture distribution that obtained by mixing the Negative Binomial (NB) distribution with the Generalized Exponential (GE) distribution. The formation of the Negative Binomial-Generalized Exponential (NB-GE) distribution and the characteristics of the Negative Binomial-Generalized Exponential (NB-GE) distribution such as the probability density function, kth moment, mean, variance, skewness and kurtosis are discussed in this paper. Estimation of the parameters from the Negative Binomial-Generalized Exponential (NB-GE) distribution using the maximum likelihood method. As an illustration, Negative Binomial-Generalized Exponential (NB-GE) distribution used to model the data of fatal crash that has more than 80% zeros.