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Asymptotic behavior of the moments of the ratio of the random sum of squares to the square of the random sum

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  • Ladoucette, Sophie A.

Abstract

Let {X1,X2,...} be a sequence of independent and identically distributed positive random variables of Pareto-type and let be a mixed Poisson process independent of the Xi's. For any fixed t[greater-or-equal, slanted]0, define:if N(t)[greater-or-equal, slanted]1 and TN(t):=0 otherwise. We determine the asymptotic behavior of any moment as t-->[infinity] with . Our method relies on the theory of functions of regular variation and an integral representation of these moments.

Suggested Citation

  • Ladoucette, Sophie A., 2007. "Asymptotic behavior of the moments of the ratio of the random sum of squares to the square of the random sum," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1021-1033, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:1021-1033
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    Cited by:

    1. Sophie A. Ladoucette & Jef L. Teugels, 2007. "Asymptotics for Ratios with Applications to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 225-242, June.
    2. Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Risks, MDPI, vol. 2(3), pages 1-26, July.

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