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Open AccessArticle

A New Heavy Tailed Class of Distributions Which Includes the Pareto

1
Department of Statistics, Central University of Rajasthan, Kishangarh 305817, India
2
Department of Economics, Centre for Actuarial Studies, University of Melbourne, Melbourne, VIC 3010, Australia
*
Author to whom correspondence should be addressed.
Risks 2019, 7(4), 99; https://doi.org/10.3390/risks7040099
Received: 23 June 2019 / Revised: 8 September 2019 / Accepted: 10 September 2019 / Published: 20 September 2019
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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. View Full-Text
Keywords: pareto distribution; excess-of-loss reinsurance; loggamma distribution; composite models pareto distribution; excess-of-loss reinsurance; loggamma distribution; composite models
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Bhati, D.; Calderín-Ojeda, E.; Meenakshi, M. A New Heavy Tailed Class of Distributions Which Includes the Pareto. Risks 2019, 7, 99.

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