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A New Generalization of the Pareto Distribution and Its Application to Insurance Data

Author

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  • Mohamed E. Ghitany

    (Department of Statistics and Operations Research, Faculty of Science, Kuwait University, Safat 13060, Kuwait)

  • Emilio Gómez-Déniz

    (Department of Quantitative Methods and TiDES Institute, University of Las Palmas de Gran Canaria, 35017 Gran Canaria, Spain)

  • Saralees Nadarajah

    (School of Mathematics, University of Manchester, Manchester M13 9PL, UK)

Abstract

The Pareto classical distribution is one of the most attractive in statistics and particularly in the scenario of actuarial statistics and finance. For example, it is widely used when calculating reinsurance premiums. In the last years, many alternative distributions have been proposed to obtain better adjustments especially when the tail of the empirical distribution of the data is very long. In this work, an alternative generalization of the Pareto distribution is proposed and its properties are studied. Finally, application of the proposed model to the earthquake insurance data set is presented.

Suggested Citation

  • Mohamed E. Ghitany & Emilio Gómez-Déniz & Saralees Nadarajah, 2018. "A New Generalization of the Pareto Distribution and Its Application to Insurance Data," JRFM, MDPI, vol. 11(1), pages 1-14, February.
    • Handle: RePEc:gam:jjrfmx:v:11:y:2018:i:1:p:10-:d:130653
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    References listed on IDEAS

    as
    1. Guo, Xu & Wong, Wing-Keung, 2016. "Multivariate Stochastic Dominance for Risk Averters and Risk Seekers," MPRA Paper 70637, University Library of Munich, Germany.
    2. Brazauskas, Vytaras & Serfling, Robert, 2003. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 365-381, November.
    3. Rytgaard, Mette, 1990. "Estimation in the Pareto Distribution," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 201-216, November.
    4. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
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    Cited by:

    1. Rashad A. R. Bantan & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2020. "On a New Result on the Ratio Exponentiated General Family of Distributions with Applications," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    2. Deepesh Bhati & Enrique Calderín-Ojeda & Mareeswaran Meenakshi, 2019. "A New Heavy Tailed Class of Distributions Which Includes the Pareto," Risks, MDPI, vol. 7(4), pages 1-17, September.
    3. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.
    4. James Allison & Bojana Milošević & Marko Obradović & Marius Smuts, 2022. "Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization," Computational Statistics, Springer, vol. 37(1), pages 403-418, March.

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