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On a New Mixed Pareto–Weibull Distribution: Its Parametric Regression Model with an Insurance Applications

Author

Listed:
  • Deepesh Bhati

    (Central University of Rajasthan)

  • Buddepu Pavan

    (Central University of Rajasthan)

  • Girish Aradhye

    (Central University of Rajasthan)

Abstract

This article introduces a new probability distribution suitable for modeling heavy-tailed and right-skewed data sets. The proposed distribution is derived from the continuous mixture of the scale parameter of the Pareto family with the Weibull distribution. Analytical expressions for various distributional properties and actuarial risk measures of the proposed model are derived. The applicability of the proposed model is assessed using two real-world insurance data sets, and its performance is compared with the existing class of heavy-tailed models. The proposed model is assumed for the response variable in parametric regression modeling to account for the heterogeneity of individual policyholders. The Expectation-Maximization (EM) Algorithm is included to expedite the process of finding maximum likelihood (ML) estimates for the parameters of the proposed models. Real-world data application demonstrates that the proposed distribution performs well compared to its competitor models. The regression model utilizing the mixed Pareto–Weibull response distribution, characterized by regression structures for both the mean and dispersion parameters, demonstrates superior performance when compared to the Pareto–Weibull regression model, where the dispersion parameter depends on covariates.

Suggested Citation

  • Deepesh Bhati & Buddepu Pavan & Girish Aradhye, 2024. "On a New Mixed Pareto–Weibull Distribution: Its Parametric Regression Model with an Insurance Applications," Annals of Data Science, Springer, vol. 11(6), pages 2077-2107, December.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:6:d:10.1007_s40745-023-00502-3
    DOI: 10.1007/s40745-023-00502-3
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    References listed on IDEAS

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    1. David Scollnik, 2007. "On composite lognormal-Pareto models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2007(1), pages 20-33.
    2. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
    3. Enrique Calderín-Ojeda & Chun Fung Kwok, 2016. "Modeling claims data with composite Stoppa models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(9), pages 817-836, October.
    4. Beirlant, Jan & Goegebeur, Yuri & Verlaak, Robert & Vynckier, Petra, 1998. "Burr regression and portfolio segmentation," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 231-250, December.
    5. Bladt, Martin, 2022. "Phase-Type Distributions For Claim Severity Regression Modeling," ASTIN Bulletin, Cambridge University Press, vol. 52(2), pages 417-448, May.
    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. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
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