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MODELLING INSURANCE DATA WITH THE PARETO ARCTAN DISTRIBUTION

Published online by Cambridge University Press:  19 June 2015

Emilio Gómez-Déniz  and
Enrique Calderín-Ojeda
Emilio Gómez-Déniz*
Affiliation:
Department of Quantitative Methods in Economics and TiDES Institute, University of Las Palmas de Gran Canaria, Spain
Enrique Calderín-Ojeda
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Australia E-Mail: ecalderin@unimelb.edu.au
*
E-Mail: emilio.gomez-deniz@ulpgc.es
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Abstract

In this paper, a new methodology based on the use of the inverse of the circular tangent function that allows us to add a scale parameter (say α) to an initial survival function is presented. The latter survival function is determined as limiting case when α tends to zero. By choosing as parent the classical Pareto survival function, the Pareto ArcTan (PAT) distribution is obtained. After providing a comprehensive analysis of its statistical properties, theoretical results with reference to insurance are illustrated. Its performance is compared, by means of the well-known Norwegian fire insurance data, with other existing heavy-tailed distributions in the literature such as Pareto, Stoppa, Shifted Lognormal, Inverse Gamma and Fréchet distributions.

Keywords

Limited expected valuelossPareto distributionshifted lognormal distributionStoppa sistributionthreshold
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 3 , September 2015 , pp. 639 - 660
Copyright
Copyright © Astin Bulletin 2015 

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