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Modelling Insurance Data With The Pareto Arctan Distribution

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  • Gómez-Déniz, Emilio
  • Calderín-Ojeda, Enrique

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.

Suggested Citation

  • Gómez-Déniz, Emilio & Calderín-Ojeda, Enrique, 2015. "Modelling Insurance Data With The Pareto Arctan Distribution," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 639-660, September.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:03:p:639-660_00
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