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Useful moment and CDF formulations for the COM–Poisson distribution

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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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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    Saralees Nadarajah

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  1. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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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

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