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Mixed Poisson distributions tail equivalent to their mixing distributions

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  • Perline, Richard

Abstract

A mixed Poisson distribution can have an upper tail asymptotically equal to the upper tail of its mixing distribution. Two broad classes of mixing distributions that generate mixed Poisson distributions with this property are identified: unbounded, non-negative distributions with mild regularity conditions that satisfy either (a) the von Mises condition for the Fréchet extreme value domain of attraction; or (b) the von Mises condition for the Gumbel extreme value domain of attraction and have hazard rates f(t)/(1 - F(t)) of order o(t-b) for some as t --> [infinity]. The Pareto distribution is prototypical of class (a) and the lognormal of class (b).

Suggested Citation

  • Perline, Richard, 1998. "Mixed Poisson distributions tail equivalent to their mixing distributions," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 229-233, June.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:3:p:229-233
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    Cited by:

    1. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    2. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    3. Tzougas, George & Hong, Natalia & Ho, Ryan, 2022. "Mixed poisson regression models with varying dispersion arising from non-conjugate mixing distributions," LSE Research Online Documents on Economics 113616, London School of Economics and Political Science, LSE Library.

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