Credibility evaluation for the exponential dispersion family

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It has long been established that under regularity conditions, the linear credibility formula with an appropriate credibility factor produces exact fair premium for claims or losses whose distribution is a member of the natural exponential family. Recently, this result has been extended to a richer family of distribution, the exponential dispersion family which 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. In this paper neither λ is regarded known, nor a fully specified prior distribution for λ is assumed. Instead, by establishing a link between the m.s.e. of the linear credibility and Fisher information we derive optimal credibility for the case where only the mean and variance of λ are specified.

Original languageEnglish
Pages (from-to)23-29
Number of pages7
JournalInsurance: Mathematics and Economics
Issue number1-2
StatePublished - 31 Mar 1999


  • Credibility formula
  • Exponential dispersion family
  • Fair premium
  • Fisher information
  • Maximum entropy
  • Optimal credibility factor

ASJC Scopus subject areas

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


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