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Natural exponential families and self-decomposability

Author

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  • Bar-Lev, Shaul K.
  • Bshouty, Daoud
  • Letac, Gérard

Abstract

Let be a full natural exponential family on which is generated by a self-decomposable probability distribution P. We provide a necessary and sufficient condition on P under which all other elements of are also self-decomposable. Moreover, we show that if is self-decomposable (i.e., composed of self-decomposable elements), then the exponential dispersion model generated by shares the same property. The statistical importance of such results is linked to the fact that self-decomposable distributions are absolutely continuous and unimodal, thus providing potential exponential dispersion models for modeling data stemming from absolutely continuous and unimodal populations.

Suggested Citation

  • Bar-Lev, Shaul K. & Bshouty, Daoud & Letac, Gérard, 1992. "Natural exponential families and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 147-152, January.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:2:p:147-152
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    Cited by:

    1. Mariani, Maria C. & Tweneboah, Osei K., 2016. "Stochastic differential equations applied to the study of geophysical and financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 170-178.
    2. Shaul K. Bar-Lev, 2023. "The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments," Mathematics, MDPI, vol. 11(20), pages 1-23, October.

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