Abstract
The Poisson distribution is as important for discrete events as the normal distribution is to large sample data. In this note, we discuss a generalized Poisson distribution recently introduced in the statistics literature. We derive—for the first time—exact and explicit expressions for its moments and the cumulative distribution function for the case of over-dispersion. Computational issues are discussed to show the real value of these expressions.
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Nadarajah, S. Useful moment and CDF formulations for the COM–Poisson distribution. Stat Papers 50, 617–622 (2009). https://doi.org/10.1007/s00362-007-0089-9
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DOI: https://doi.org/10.1007/s00362-007-0089-9