Exponential dispersion models and credibility

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The Exponential Dispersion Family is a rich family of distributions, comprised of several distributions, some of which are heavy-tailed and as such could be of significant relevance to actuarial science. The family draws its richness from a dispersion parameter σ2 = 1/λ which is equal to 1 in the case of the Natural Exponential Family. We consider three cases. In the first λ is assumed known, in the second a prior distribution for λ is given, and in the third the prior distribution of λ is not known and is derived by means of the maximum entropy principle, assuming the prior mean of λ can be specified. For these cases, a conjugate prior distribution for the risk parameter is assumed and credibility formulae are derived for the estimation of the fair premium.

Original languageEnglish
Pages (from-to)89-96
Number of pages8
JournalScandinavian Actuarial Journal
Issue number1
StatePublished - 1 Jan 1998


  • Credibility formula
  • Exponential dispersion family
  • Fair premium
  • Maximum entropy

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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