The zero inflated negative binomial-beta exponential (ZINB-BE) distribution is developed, it is an alternative distribution for the excessive zero counts with overdispersion. The ZINB-BE distribution is a mixture of two distributions which are Bernoulli and negative binomial-beta exponential distributions. In this work, some characteristics of the proposed distribution are presented, such as, mean and variance. The maximum likelihood estimation is applied to parameter estimation of the proposed distribution. Finally some results of Monte Carlo simulation study, it seems to have high-efficiency when the sample size is large.
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