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Credible Means are exact Bayesian for Exponential Families

Published online by Cambridge University Press:  29 August 2014

William S. Jewell
William S. Jewell*
Affiliation:
University of California, Berkeley and Teknekron, Inc
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Abstract

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The credibility formula used in casualty insurance experience rating is known to be exact for certain prior-likelihood distributions, and is the minimum least-squares unbiased estimator for all others. We show that credibility is, in fact, exact for all simple exponential families where the mean is the sufficient statistic, and is also exact in an extended sense for all regular distributions with their natural conjugate priors where there is a fixed-dimensional sufficient statistic.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 8 , Issue 1 , September 1974 , pp. 77 - 90
Copyright
Copyright © International Actuarial Association 1974

References

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