• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.463-477
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• 2009

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.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.2
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• pp.43-51
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• 2011

Probabilistic seismic hazard analysis (PSHA), which can effectively apply inevitable uncertainties in seismic data, considers a number of seismotectonic models and attenuation equations. The calculated hazard by PSHA is generally a value dependent on peak ground acceleration (PGA) and expresses the value as an annual exceedance probability. To represent the uncertainty range of a hazard which has occurred using various seismic data, a hazard curve figure shows both a mean curve and percentile curves (15, 50, and 85). The percentile performs an important role in that it indicates the uncertainty range of the calculated hazard, could be calculated using various methods by the relation of the weight and hazard. This study using the weight accumulation method, the weighted hazard method, the maximum likelihood method, and the moment method, has calculated the percentile of the computed hazard by PSHA on the Shinuljin 1, 2 site. The calculated percentile using the weight accumulation method, the weighted hazard method, and the maximum likelihood method, have similar trends and represent the range of all computed hazards by PSHA. The calculated percentile using the moment method effectively showed the range of hazards at the source which includes a site. This study suggests the moment method as effective percentile calculation method considering the almost same mean hazard for the seismotectonic model and a source which includes a site.