Natural exponential families and self-decomposability

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

Statistics & Probability Letters, 1992, vol. 13, issue 2, 147-152

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.

Keywords: Self-decomposable; distribution; unimodal; distribution; infinitely; divisible; distribution; natural; exponential; family; exponential; dispersion; model (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (2)

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