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Modelling losses and locating the tail with the Pareto Positive Stable distribution

Montserrat Guillen, Faustino Prieto and José María Sarabia ()

Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 454-461

Abstract: This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.

Keywords: Pareto distribution; Positive stable law; Loss model; Severity distribution (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (22)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:49:y:2011:i:3:p:454-461

DOI: 10.1016/j.insmatheco.2011.07.004

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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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