IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i9p156-d1229854.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/9/156/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-9091/11/9/156/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Min Deng & Mostafa Aminzadeh & Min Ji, 2021. "Bayesian Predictive Analysis of Natural Disaster Losses," Risks, MDPI, vol. 9(1), pages 1-23, January.
    2. Bowen Liu & Malwane M. A. Ananda, 2022. "A Generalized Family of Exponentiated Composite Distributions," Mathematics, MDPI, vol. 10(11), pages 1-18, June.
    3. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    4. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    5. Ahmed Z. Afify & Ahmed M. Gemeay & Noor Akma Ibrahim, 2020. "The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    6. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    7. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    8. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.
    9. Semhar Michael & Tatjana Miljkovic & Volodymyr Melnykov, 2020. "Mixture modeling of data with multiple partial right-censoring levels," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 355-378, June.
    10. Blostein, Martin & Miljkovic, Tatjana, 2019. "On modeling left-truncated loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 35-46.
    11. Muhammad Hilmi Abdul Majid & Kamarulzaman Ibrahim & Nurulkamal Masseran, 2023. "Three-Part Composite Pareto Modelling for Income Distribution in Malaysia," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    12. Naderi, Mehrdad & Hashemi, Farzane & Bekker, Andriette & Jamalizadeh, Ahad, 2020. "Modeling right-skewed financial data streams: A likelihood inference based on the generalized Birnbaum–Saunders mixture model," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    13. Carmine Franco & Luc Dumontier, 2024. "Modelling capacity for systematic equity strategies," Journal of Asset Management, Palgrave Macmillan, vol. 25(4), pages 407-416, July.
    14. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    15. Chen, Zezhun & Dassios, Angelos & Tzougas, George, 2022. "EM estimation for the bivariate mixed exponential regression model," LSE Research Online Documents on Economics 115132, London School of Economics and Political Science, LSE Library.
    16. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    17. Jackie Li & Jia Liu, 2023. "Claims Modelling with Three-Component Composite Models," Risks, MDPI, vol. 11(11), pages 1-16, November.
    18. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    19. Eling, Martin & Loperfido, Nicola, 2017. "Data breaches: Goodness of fit, pricing, and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 126-136.
    20. Zoia, Maria Grazia & Biffi, Paola & Nicolussi, Federica, 2018. "Value at risk and expected shortfall based on Gram-Charlier-like expansions," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 92-104.

    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:gam:jrisks:v:11:y:2023:i:9:p:156-:d:1229854. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.