The closed form and the factorial moment of the NB-GE distribution
are derived. The NB-GE distribution appropriate when we find the one
related to count data which have a large number of zeros and overdispersion
in Poisson distribution. In addition, we present the basic properties
of the new distribution such as mean, variance, skewness and kurtosis.
Including, the negative binomial-exponential distributions are presented
as special cases of this NB-GE distribution. Parameters estimation is
also implemented using maximum likelihood method and the usefulness
of the NB-GE distribution is illustrated by real data set. When using a
goodness of fit test, the results show that the NB-GE distribution can
provide a better fit than the NB distribution and Poisson distribution
for count data that contain a large number of zeros.