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On Poisson–Tweedie mixtures

Author

Listed:
  • Vladimir V. Vinogradov

    (Ohio University)

  • Richard B. Paris

    (Abertay University)

Abstract

Poisson-Tweedie mixtures are the Poisson mixtures for which the mixing measure is generated by those members of the family of Tweedie distributions whose support is non-negative. This class of non-negative integer-valued distributions is comprised of Neyman type A, back-shifted negative binomial, compound Poisson-negative binomial, discrete stable and exponentially tilted discrete stable laws. For a specific value of the “power” parameter associated with the corresponding Tweedie distributions, such mixtures comprise an additive exponential dispersion model. We derive closed-form expressions for the related variance functions in terms of the exponential tilting invariants and particular special functions. We compare specific Poisson-Tweedie models with the corresponding Hinde-Demétrio exponential dispersion models which possess a comparable unit variance function. We construct numerous local approximations for specific subclasses of Poisson-Tweedie mixtures and identify Lévy measure for all the members of this three-parameter family.

Suggested Citation

  • Vladimir V. Vinogradov & Richard B. Paris, 2017. "On Poisson–Tweedie mixtures," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-23, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0068-1
    DOI: 10.1186/s40488-017-0068-1
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    References listed on IDEAS

    as
    1. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    2. Bent Jørgensen & Célestin Kokonendji, 2016. "Discrete dispersion models and their Tweedie asymptotics," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 43-78, January.
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