Robust and efficient fitting of severity models and the method of Winsorized Moments

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<title>Robust and efficient fitting of severity models and the method of Winsorized Moments</title>
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<namePart>Ghorai, Jugal</namePart>
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<abstract displayLabel="Summary">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 from1925 to 1995. In particular, the estimated pure premiums for an insurance layer are computedwhen the lognormal and log-logistic models are fitted to the data using the MWM, MTM and MLE methods.</abstract>
<note type="statement of responsibility">Qian Zhao, Vytaras Brazauskas, Jugal Ghorai</note>
<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080592042">
<topic>Modelos matemáticos</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080592011">
<topic>Modelos actuariales</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080602437">
<topic>Matemática del seguro</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080579258">
<topic>Cálculo actuarial</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
<identifier type="local">MAP20077000420</identifier>
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<text>01/01/2018 Volumen 48 Número 1 - enero 2018 , p. 275-309</text>
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