High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the Poisson distribution is the most common distribution used to model count data. However, due to the Poisson distribution's reliance on a single parameter (the mean), data exhibiting overdispersion or underdispersion under the Poisson model must be modeled under alternative distributions to account for these statistically significant deviations. Typically, the negative binomial distribution is used to model data with over-dispersion, however the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution provides an improved, yet relatively unknown, alternative. In particular, the CMP distribution is suitable for over and under-dispersed data, and is a member of the exponential family, which has many favorable properties.

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