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A New Heavy Tailed Class of Distributions Which Includes the Pareto

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  • Deepesh Bhati

    (Department of Statistics, Central University of Rajasthan, Kishangarh 305817, India)

  • Enrique Calderín-Ojeda

    (Department of Economics, Centre for Actuarial Studies, University of Melbourne, Melbourne, VIC 3010, Australia)

  • Mareeswaran Meenakshi

    (Department of Statistics, Central University of Rajasthan, Kishangarh 305817, India)

Abstract

In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:4:p:99-:d:269272
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    References listed on IDEAS

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    2. 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.
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    6. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
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    Cited by:

    1. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.

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