MODELLING INSURANCE DATA WITH THE PARETO ARCTAN DISTRIBUTION

E-ISSN： 1783-1350|45|3|639-660

ISSN： 0515-0361

Source： ASTIN Bulletin, Vol.45, Iss.3, 2015-06, pp. : 639-660

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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.