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Bayesian Inference for the Loss Models via Mixture Priors

Author

Listed:
  • Min Deng

    (Department of Mathematics, Towson University, Towson, MD 21252, USA)

  • Mostafa S. Aminzadeh

    (Department of Mathematics, Towson University, Towson, MD 21252, USA)

Abstract

Constructing an accurate model for insurance losses is a challenging task. Researchers have developed various methods to model insurance losses, such as composite models. Composite models combine two distributions: one for part of the data with small and high frequencies and the other for large values with low frequencies. The purpose of this article is to consider a mixture of prior distributions for exponential–Pareto and inverse-gamma–Pareto composite models. The general formulas for the posterior distribution and the Bayes estimator of the support parameter θ are derived. It is shown that the posterior distribution is a mixture of individual posterior distributions. Analytic results and Bayesian inference based on the proposed mixture prior distribution approach are provided. Simulation studies reveal that the Bayes estimator with a mixture distribution outperforms the Bayes estimator without a mixture distribution and the ML estimator regarding their accuracies. Based on the proposed method, the insurance losses from natural events, such as floods from 2000 to 2019 in the USA, are considered. As a measure of goodness-of-fit, the Bayes factor is used to choose the best-fitted model.

Suggested Citation

  • Min Deng & Mostafa S. Aminzadeh, 2023. "Bayesian Inference for the Loss Models via Mixture Priors," Risks, MDPI, vol. 11(9), pages 1-27, August.
  • Handle: RePEc:gam:jrisks:v:11:y:2023:i:9:p:156-:d:1229854
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    References listed on IDEAS

    as
    1. M. S. Aminzadeh & M. Deng, 2019. "Bayesian predictive modeling for Inverse Gamma-Pareto composite distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1938-1954, April.
    2. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    3. Abu Bakar, S.A. & Hamzah, N.A. & Maghsoudi, M. & Nadarajah, S., 2015. "Modeling loss data using composite models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 146-154.
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