A New Heavy Tailed Class of Distributions Which Includes the Pareto

Deepesh Bhati, Enrique Calderín-Ojeda and Mareeswaran Meenakshi
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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

Risks, 2019, vol. 7, issue 4, 1-17

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.

Keywords: pareto distribution; excess-of-loss reinsurance; loggamma distribution; composite models (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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