Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T13:15:50.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Scale Mixtures Distributions in Insurance Applications

Published online by Cambridge University Press:  17 April 2015

S.T. Boris Choy  and
C.M. Chan
S.T. Boris Choy
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Email: [email protected]
C.M. Chan
Affiliation:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. Email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper non-normal distributions via scale mixtures are introduced into insurance applications. The symmetric distributions of interest are the Student-t and exponential power (EP) distributions. A Bayesian approach is adopted with the aid of simulation to obtain posterior summaries. We shall show that the computational burden for the Bayesian calculations is alleviated via the scale mixtures representations. Illustrative examples are given.

Keywords

Normal DistributionStudent-t DistributionExponential Power DistributionScale mixtures of Normal DistributionsScale Mixtures of Uniform distributionsMarkov chain Monte CarloGibbs SamplerPure PremiumCredibilityRobustnessOutliers
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 1 , May 2003 , pp. 93 - 104
Copyright
Copyright © ASTIN Bulletin 2003

References

Andrews, D.F. and Mallows, C.L. (1974) Scale mixtures of normal distributions. Journal of the Royal Statistical Society, Ser. B, 36, 99–102.Google Scholar
Berger, J.O. (1994) An overview of robust Bayesian analysis (with discussion). TEST 1, 5–124.Google Scholar
Box, G.E.P. and Tiao, G.C. (1992) Bayesian Inference in Statistical Analysis. Addison Wesley, Massachusettes.Google Scholar
Bühlman, H. and Straub, E. (1972) Credibility for Loss ratios. English Translation in ARCH.Google Scholar
Choy, S.T.B. (1999) Contribution to the discussion of ‘Robustifying Bayesian Procedures’ by Walker, S.G. and Gutierrez-Pena, E. In Bayesian Statistics 6 (eds. Bernardo, J.M., Berger, J.O., Dawid, A.P. and Smith, A.F.M., pp. 685–710, Oxford University Press, New York.Google Scholar
Choy, S.T.B. and Smith, A.F.M. (1997) Hierarchical models with scale mixtures of normal distributions. TEST 6, 205–221.CrossRefGoogle Scholar
Choy, S.T.B. and Walker, S.G. (1998) “The Extended Exponential Power Distribution and Bayesian Robustness”. Technical Report, University of Hong Kong.Google Scholar
Gelfand, A.E., Hills, S.E., Racine-Poon, A. and Smith, A.F.M. (1990). Illustration of Bayesian inference in normal models using Gibbs sampling. Journal of the American Statistical Association 85, 972–985.CrossRefGoogle Scholar
Herzog, T.N. (1996) Introduction to Credibility Theory. Second edition. ACTEX Publications, USA.Google Scholar
Klugman, S.A. (1992) Bayesian Statistics in Actuarial Science: With Emphasis on Credibility. Kluwer Academic Publishers, Massachusetts.CrossRefGoogle Scholar
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (1998) Loss Models: From Data to Decisions. Wiley, New York.Google Scholar
Landsman, Z. and Makov, U.E. (1998) Exponential dispersion models and credibility. Scandinavian Actuarial Journal 1, 89–96.Google Scholar
Landsman, Z. and Makov, U.E. (1999) Sequential credibility evaluation for symmetric location claim distributions. Insurance: Mathematics and Economics 24, 291–300.Google Scholar
Meyers, G. (1984) Empirical Bayesian Credibility for Workers’ Compensation Classification Ratemaking. Proceedings of the Casualty Actuarial Society 71, 96–121.Google Scholar
Smith, A.F.M. and Roberts, G.O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo method. Journal of the Royal Statistical Society, Ser. B 55, 3–24.Google Scholar
Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). The Annals of Statistics 22, 1701–1762.Google Scholar
Walker, S.G. and Gutierrez-Pena, E. (1999) Robustifying Bayesian Procedures (with discussion). In Bayesian Statistics 6 (eds. Bernardo, J.M., Berger, J.O. Dawid, A.P. and Smith, A.F.M. pp. 685–710, Oxford University Press, New York.Google Scholar
Young, V.R. (1997) Credibility using semiparametric models. ASTIN Bulletin 27, 273–285.CrossRefGoogle Scholar
Young, V.R. (1998) Robust Bayesian credibility using semiparametric models. ASTIN Bulletin, 28, 187–203.CrossRefGoogle Scholar