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A Weighted Poisson Distribution for Underdispersed Count Data

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  • Chedly Gelin Louzayadio
  • Rodnellin Onesime Malouata
  • Michel Diafouka Koukouatikissa

Abstract

In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y)- Clearly, the recorded y is not an observation on Y, but on the random variable Yw, which is said to be the weighted version of Y. This distribution has three parameters and belongs to the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.

Suggested Citation

  • Chedly Gelin Louzayadio & Rodnellin Onesime Malouata & Michel Diafouka Koukouatikissa, 2021. "A Weighted Poisson Distribution for Underdispersed Count Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 157-157, July.
    • Handle: RePEc:ibn:ijspjl:v:10:y:2021:i:4:p:157
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    References listed on IDEAS

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    1. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    2. Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
    3. R. W. Morgan, 1975. "Some Stochastic Models to Describe the Fertilization of an Egg," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(1), pages 137-138, March.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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