IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v15y2022i11p500-d954772.html
   My bibliography  Save this article

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

Author

Listed:
  • Abbas Mahdavi

    (Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran)

  • Omid Kharazmi

    (Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran)

  • Javier E. Contreras-Reyes

    (Instituto de Estadística, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso 2360102, Chile)

Abstract

Deriving loss distribution from insurance data is a challenging task, as loss distribution is strongly skewed with heavy tails with some levels of outliers. This paper extends the weighted exponential (WE) family to the contaminated WE (CWE) family, which offers many flexible features, including bimodality and a wide range of skewness and kurtosis. We adopt Expectation-Maximization (EM) and Bayesian approaches to estimate the model, providing the likelihood and the priors for all unknown parameters. Finally, two sets of claims data are analyzed to illustrate the efficiency of the proposed method in detecting outliers.

Suggested Citation

  • Abbas Mahdavi & Omid Kharazmi & Javier E. Contreras-Reyes, 2022. "On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data," JRFM, MDPI, vol. 15(11), pages 1-18, October.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:11:p:500-:d:954772
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/15/11/500/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/15/11/500/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2021. "On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Younshik Chung & Chansoo Kim, 2004. "Measuring robustness for weighted distributions: Bayesian perspective," Statistical Papers, Springer, vol. 45(1), pages 15-31, January.
    3. Antonio Punzo & Angelo Mazza & Antonello Maruotti, 2018. "Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(14), pages 2563-2584, October.
    4. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    5. Contreras-Reyes, Javier E. & López Quintero, Freddy O. & Wiff, Rodrigo, 2018. "Bayesian modeling of individual growth variability using back-calculation: Application to pink cusk-eel (Genypterus blacodes) off Chile," Ecological Modelling, Elsevier, vol. 385(C), pages 145-153.
    6. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    7. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    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. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    2. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    3. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    4. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    5. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    6. Cheung, Ka Chun & Phillip Yam, Sheung Chi & Yuen, Fei Lung & Zhang, Yiying, 2020. "Concave distortion risk minimizing reinsurance design under adverse selection," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 155-165.
    7. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    8. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    9. Catalina Bolancé & Montserrat Guillén & Alemar Padilla, 2015. "Estimación del riesgo mediante el ajuste de cópulas," Working Papers 2015-01, Universitat de Barcelona, UB Riskcenter.
    10. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Impact of Dependence on Some Multivariate Risk Indicators," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 395-427, June.
    11. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    12. Das Bikramjit & Fasen-Hartmann Vicky, 2019. "Conditional excess risk measures and multivariate regular variation," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 1-23, December.
    13. Ji, Liuyan & Tan, Ken Seng & Yang, Fan, 2021. "Tail dependence and heavy tailedness in extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 282-293.
    14. repec:hal:wpaper:hal-01171395 is not listed on IDEAS
    15. Cossette, Hélène & Landriault, David & Marceau, Etienne & Moutanabbir, Khouzeima, 2012. "Analysis of the discounted sum of ascending ladder heights," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 393-401.
    16. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2017. "Reserve modelling and the aggregation of risks using time varying copula models," Economic Modelling, Elsevier, vol. 67(C), pages 149-158.
    17. Gareth W. Peters & Rodrigo S. Targino & Mario V. Wüthrich, 2017. "Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks," Risks, MDPI, vol. 5(4), pages 1-51, September.
    18. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre & Veilleux, Déry, 2018. "Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 53-71.
    19. Willmot, Gordon E. & Woo, Jae-Kyung, 2012. "On the analysis of a general class of dependent risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 134-141.
    20. Areski Cousin & Elena Di Bernardino, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
    21. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.

    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:jjrfmx:v:15:y:2022:i:11:p:500-:d:954772. 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.