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ROBUST AND EFFICIENT FITTING OF SEVERITY MODELS AND THE METHOD OF WINSORIZED MOMENTS

Published online by Cambridge University Press:  02 November 2017

Qian Zhao ,
Vytaras Brazauskas  and
Jugal Ghorai
Qian Zhao
Affiliation:
Department of Mathematics, Robert Morris University, Moon Township, PA 15108, USA, E-Mail: zhao@rmu.edu
Vytaras Brazauskas*
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
Jugal Ghorai
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA, E-Mail: jugal@uwm.edu
*
E-Mail: vytaras@uwm.edu
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Abstract

Continuous parametric distributions are useful tools for modeling and pricing insurance risks, measuring income inequality in economics, investigating reliability of engineering systems, and in many other areas of application. In this paper, we propose and develop a new method for estimation of their parameters—the method of Winsorized moments (MWM)—which is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for log-location-scale families and their variants, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their performance is also compared to that of MTM and the maximum likelihood estimators (MLE). In addition, the effect of model choice and parameter estimation method on risk pricing is illustrated using actual data that represent hurricane damages in the United States from 1925 to 1995. In particular, the estimated pure premiums for an insurance layer are computed when the lognormal and log-logistic models are fitted to the data using the MWM, MTM and MLE methods.

Keywords

Claim severityefficiencyinsurance layerrobustnesswinsorized data
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 275 - 309
Copyright
Copyright © Astin Bulletin 2017 

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