IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v8y1974i01p77-90_00.html
   My bibliography  Save this article

Credible Means are exact Bayesian for Exponential Families

Author

Listed:
  • Jewell, William S.

Abstract

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.

Suggested Citation

  • Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    • Handle: RePEc:cup:astinb:v:8:y:1974:i:01:p:77-90_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036100009193/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gómez-Déniz, E., 2008. "A generalization of the credibility theory obtained by using the weighted balanced loss function," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 850-854, April.
    2. Georgios Pitselis, 2024. "Credibility Distribution Estimation with Weighted or Grouped Observations," Risks, MDPI, vol. 12(1), pages 1-27, January.
    3. Jeong Himchan & Valdez Emiliano A., 2020. "Bayesian credibility premium with GB2 copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 157-171, January.
    4. Alicja Wolny-Dominiak & Tomasz Żądło, 2021. "The Measures of Accuracy of Claim Frequency Credibility Predictor," Sustainability, MDPI, vol. 13(21), pages 1-13, October.
    5. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    6. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2018. "Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims," Risks, MDPI, vol. 6(2), pages 1-11, April.
    7. Xacur, Oscar Alberto Quijano & Garrido, José, 2018. "Bayesian credibility for GLMs," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 180-189.
    8. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    9. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    10. Landsman, Zinoviy, 2002. "Credibility theory: a new view from the theory of second order optimal statistics," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 351-362, June.
    11. Bennett, Daniel & Chiang, Chun-Fang & Malani, Anup, 2015. "Learning during a crisis: The SARS epidemic in Taiwan," Journal of Development Economics, Elsevier, vol. 112(C), pages 1-18.
    12. Landsman, Zinoviy & Makov, Udi E., 1999. "Credibility evaluation for the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 23-29, March.
    13. Pérez-Hornero, Patricia & Arias-Nicolás, José Pablo & Pulgarín, Antonio A. & Pulgarín, Antonio, 2013. "An annual JCR impact factor calculation based on Bayesian credibility formulas," Journal of Informetrics, Elsevier, vol. 7(1), pages 1-9.
    14. Marina Maniati & Evangelos Sambracos, 2017. "Decision-making process in shipping finance: A stochastic approach," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1317083-131, January.
    15. Paulsen, Jostein & Lunde, Astrid & Skaug, Hans Julius, 2008. "Fitting mixed-effects models when data are left truncated," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 121-133, August.
    16. Jeong Himchan & Valdez Emiliano A., 2020. "Bayesian credibility premium with GB2 copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 157-171, January.
    17. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2022. "Effective experience rating for large insurance portfolios via surrogate modeling," Papers 2211.06568, arXiv.org, revised Jun 2024.
    18. Gómez-Déniz, E., 2018. "Adding a parameter to the exponential and Weibull distributions with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 108-119.
    19. Landsman, Zinoviy & Makov, Udi E., 2000. "On credibility evaluation and the tail area of the exponential dispersion family," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 277-283, December.
    20. Kim, Joseph H.T. & Jeon, Yongho, 2013. "Credibility theory based on trimming," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 36-47.
    21. Pitselis, Georgios, 2013. "Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 391-403.
    22. Sánchez-Sánchez, M. & Sordo, M.A. & Suárez-Llorens, A. & Gómez-Déniz, E., 2019. "Deriving Robust Bayesian Premiums Under Bands Of Prior Distributions With Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 147-168, January.
    23. Jeong, Himchan, 2024. "Tweedie multivariate semi-parametric credibility with the exchangeable correlation," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 13-21.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:astinb:v:8:y:1974:i:01:p:77-90_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/asb .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.