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On Lévy measures for infinitely divisible natural exponential families

Author

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  • Kokonendji, Célestin C.
  • Khoudar, Mohamed

Abstract

We link the infinitely divisible measure [mu] to its modified Lévy measure [rho]=[rho]([mu]) in terms of their variance functions, where x-2[[rho](dx)-[rho]({0})[delta]0(dx)] is the Lévy measure associated with [mu]. We deduce that, if the variance function of [mu] is a polynomial of degree p[greater-or-equal, slanted]2, then, the variance function of [rho] is still a second degree polynomial. We illustrate these results with some Lévy processes such as positive stable and a class of Poisson stopped-sum processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:13:p:1364-1368
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    Cited by:

    1. Vinogradov, Vladimir, 2011. "On Kendall-Ressel and related distributions," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1493-1501, October.
    2. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    3. Bar-Lev, Shaul K. & Letac, Gérard, 2010. "The limiting behavior of some infinitely divisible exponential dispersion models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1870-1874, December.
    4. Yacouba Boubacar Maïnassara & Célestin Kokonendji, 2014. "On normal stable Tweedie models and power-generalized variance functions of only one component," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 585-606, September.

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