Natural exponential families and self-decomposability

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

Research output: Contribution to journalArticlepeer-review


Let F be a full natural exponential family on R 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 F are also self-decomposable. Moreover, we show that if F is self-decomposable (i.e., composed of self-decomposable elements), then the exponential dispersion model generated by F 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.

Original languageEnglish
Pages (from-to)147-152
Number of pages6
JournalStatistics and Probability Letters
Issue number2
StatePublished - 27 Jan 1992


  • Self-decomposable distribution
  • exponential dispersion model
  • infinitely divisible distribution
  • natural exponential family
  • unimodal distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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