THE NEGATIVE BINOMIAL-ERLANG DISTRIBUTION WITH APPLICATIONS
S. Kongrod, Winai Bodhisuwan, P. Payakkapong · International Journal of Pure and Apllied Mathematics · 2014
This paper introduces a new three-parameter of the mixed negative binomial distribution which is called the negative binomial-Erlang distribution.This distribution obtained by mixing the negative binomial distribution with the Erlang distribution.The negative binomial-Erlang distribution can be used to describe count data with a large number of zeros.The negative binomialexponential is presented as special cases of the negative binomial-Erlang distribution.In addition, we present some properties of the negative binomial-Erlang distribution including factorial moments, mean, variance, skewness and kurtosis.The parameter estimation for negative binomial-Erlang distribution by the maximum likelihood estimation are provided.Applications of the the negative binomial-Erlang distribution are carried out two real count data sets.The result shown that the negative binomial-Erlang distribution is better than fit when compared the Poisson and negative binomial distributions.