Abstract
Poisson and negative binomial distributions are frequently used to fit count data. A limitation of the Poisson distribution is that the mean and the variance are assumed to be equal, but this assumption is far from being realistic in many practical applications. The negative binomial distribution is more used in cases of overdispersion, given that their variance is higher than the mean. The two-parameter double Poisson distribution introduced by Efron may be considered as a useful alternative to the Poisson and negative binomial distributions, given that it can account for both overdispersion and under-dispersion. In this article, we obtain maximum likelihood and Bayesian estimates for the double Poisson distribution. We also extend the proposed methodology for the situation in which there is an excess of zeros in a sample. Applications of the double Poisson distribution are considered assuming simulated and real data sets.
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