Date of Award

May 2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Vytaras Brazauskas

Second Advisor

Jugal Ghorai

Committee Members

Jay Beder, Wei Wei, Dashan Fan

Keywords

Claim Severity, Risk Analysis, Robust Statistics, Trimmed Data, Winsorized Data

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 dissertation, 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 location-scale and log-location-scale families, 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, log-logistic and log-Laplace models are fitted to the data using the MWM, MTM, and MLE methods.

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