Intrinsic objective Bayesian estimation of the mean of the Tweedie family

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The Tweedie family, which is classified by the choice of power unit variance function, includes heavy tailed distributions, and as such could be of significant relevance to actuarial science. The class includes the Normal, Poisson, Gamma, Inverse Gaussian, Stable and Compound Poisson distributions. In this study, we explore the intrinsic objective Bayesian point estimator for the mean value of the Tweedie family based on the intrinsic discrepancy loss function–which is an inherent loss function arising only from the underlying distribution or model, without any subjective considerations–and the Jeffreys prior distribution, which is designed to express absence of information about the quantity of interest. We compare the proposed point estimator with the Bayes estimator, which is the posterior mean based on quadratic loss function and the Jeffreys prior distribution. We carry a numerical study to illustrate the methodology in the context of the Inverse Gaussian model, which is fully unexplored in this novel context, and which is useful to insurance contracts.

Original languageEnglish
Pages (from-to)585-603
Number of pages19
JournalScandinavian Actuarial Journal
Issue number7
StatePublished - 9 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Jeffreys prior distribution
  • Tweedie family
  • intrinsic discrepancy loss function
  • intrinsic objective Bayesian point estimator
  • intrinsic objective Bayesian risk function

ASJC Scopus subject areas

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


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