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Credibility Distribution Estimation with Weighted or Grouped Observations

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  • Georgios Pitselis

    (Department of Statistics & Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou Str. T. K., 18534 Piraeus, Greece
    Department of Mathematics & Statistics, Concordia University, 1455 De Maisonneuve Blvd. W., Montreal, QC H3G 1M8, Canada)

Abstract

In non-life insurance practice, actuaries are often faced with the challenge of predicting the number of claims and claim amounts to be incurred at any given time, which serve to implement fair pricing and reserves given the nature of the risk. This paper extends Jewell’s credible distribution in terms of forecasting the distribution of individual risk in cases where the observations are weighted or are grouped in intervals. More specifically, we show how empirical distribution functions can be embedded within Bühlmann’s and Straub’s credibility model. The optimal projection theorem is applied for credibility estimation and more insight into the derivation of the credibility distribution estimators is also provided. In addition, distribution credibility estimators are established and numerical illustrations are presented herein. Two examples of distribution credibility estimation are given, one with insurance loss data and the other with industry financial data.

Suggested Citation

  • Georgios Pitselis, 2024. "Credibility Distribution Estimation with Weighted or Grouped Observations," Risks, MDPI, vol. 12(1), pages 1-27, January.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:1:p:10-:d:1312633
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    References listed on IDEAS

    as
    1. Minwoo Kim & Himchan Jeong & Dipak Dey, 2022. "Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach," Risks, MDPI, vol. 10(3), pages 1-11, March.
    2. Zinoviy Landsman & Udi Makov, 1998. "Exponential dispersion models and credibility," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1998(1), pages 89-96.
    3. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    4. Xiaoqiang Cai & Limin Wen & Xianyi Wu & Xian Zhou, 2015. "Credibility Estimation of Distribution Functions with Applications to Experience Rating in General Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(4), pages 311-335, October.
    Full references (including those not matched with items on IDEAS)

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