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On Kendall-Ressel and related distributions

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  • Vinogradov, Vladimir

Abstract

We delineate a connection of Kendall-Ressel and related laws with the lower real branch of Lambert W function. A characterization of the canonical member of Kendall-Ressel class is found. The Letac-Mora interpretation of the reciprocity of two specific NEFs is extended by considering two related reproductive EDMs. A local limit theorem on gamma convergence for the reproductive back-shifted Kendall-Ressel EDM is derived. Each member of this EDM is self-decomposable and unimodal, but not strongly unimodal. The coefficient of variation, skewness and kurtosis of each representative of this EDM are higher than the corresponding measures for the members of gamma and inverse Gaussian EDMs. An integral representation for the lower real branch of Lambert W function is given.

Suggested Citation

  • Vinogradov, Vladimir, 2011. "On Kendall-Ressel and related distributions," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1493-1501, October.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1493-1501
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    References listed on IDEAS

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    1. Dhafer Malouche, 1998. "Natural exponential families associated to Pick functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 391-412, December.
    2. Kokonendji, Célestin C. & Khoudar, Mohamed, 2006. "On Lévy measures for infinitely divisible natural exponential families," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1364-1368, July.
    3. C. Kokonendji, Célestin, 2001. "First passage times on zero and one and natural exponential families," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 293-298, February.
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