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An extended Poisson distribution

Author

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  • Hassan S. Bakouch
  • Maher Kachour
  • Saralees Nadarajah

Abstract

The Poisson distribution is extended over the set of all integers. The motivation comes from the many reflected versions of the gamma distribution, the continuous analog of the Poisson distribution, defined over the entire real line. Various mathematical properties of the extended Poisson distribution are derived. Estimation procedures by the methods of moments and maximum likelihood are also derived with their performance assessed by simulation. Finally, a real data application is illustrated.

Suggested Citation

  • Hassan S. Bakouch & Maher Kachour & Saralees Nadarajah, 2016. "An extended Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6746-6764, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:22:p:6746-6764
    DOI: 10.1080/03610926.2014.967587
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    Cited by:

    1. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.

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