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Compound weighted Poisson distributions

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  • Leda Minkova
  • N. Balakrishnan

Abstract

In this paper, we discuss discrete compound distributions, in which the counting distribution is a weighted Poisson distribution. The over- and under-dispersion of these distributions are then discussed by analyzing the Fisher index of dispersion as well as a newly introduced factorial moment to mean measure. Several cases of compounding distributions and weight functions are subsequently examined in detail. Copyright Springer-Verlag 2013

Suggested Citation

  • Leda Minkova & N. Balakrishnan, 2013. "Compound weighted Poisson distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 543-558, May.
  • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:543-558
    DOI: 10.1007/s00184-012-0403-y
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    References listed on IDEAS

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    1. Willmot, Gord, 1986. "Mixed Compound Poisson Distributions," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 59-79, April.
    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. M. J. Goovaerts & M. Vandebroeck & R. Kaas, 1986. "Ordering Of Risks And Weighted Compound Distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(4), pages 273-282, December.
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    Cited by:

    1. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    2. Freud, Thomas & Rodriguez, Pablo M., 2023. "The Bell–Touchard counting process," Applied Mathematics and Computation, Elsevier, vol. 444(C).

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