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.
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