Comparison Study of Parameter Estimation Methods for Some Extreme Value Distributions (Focused on the Regression Method)

Title & Authors
Comparison Study of Parameter Estimation Methods for Some Extreme Value Distributions (Focused on the Regression Method)
Woo, Ji-Yong; Kim, Myung-Suk;

Abstract
Parameter estimation methods such as maximum likelihood estimation method, probability weighted moments method, regression method have been popularly applied to various extreme value models in numerous literature. Among three methods above, the performance of regression method has not been rigorously investigated yet. In this paper the regression method is compared with the other methods via Monte Carlo simulation studies for estimation of parameters of the Generalized Extreme Value(GEV) distribution and the Generalized Pareto(GP) distribution. Our simulation results indicate that the regression method tends to outperform other methods under small samples by providing smaller biases and root mean square errors for estimation of location parameter of the GEV model. For the scale parameter estimation of the GP model under small samples, the regression method tends to report smaller biases than the other methods. The regression method tends to be superior to other methods for the shape parameter estimation of the GEV model and GP model when the shape parameter is -0.4 under small and moderately large samples.
Keywords
Generalized extreme value distribution;generalized Pareto distribution, maximum likelihood estimation method;Monte Carlo simulation;probability weighted moments method;regression method;
Language
Korean
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