Estimation Procedures for the General Extreme Value Distribution for the Maxima: Alternative PWM Method

• Published in: Journal of hydrologic engineering 2012-08, Vol.17 (8), p.909-922
• Main Author: Raynal-Vellaseñor, Jose A
• Format: Article
• Language: English
• Subjects: Error analysis; Extreme values; Maxima; Parameter estimation; Parameters; Pulse duration modulation; Quantiles; Sampling; Technical Papers
• ISSN: 1084-0699; 1943-5584
• DOI: 10.1061/(ASCE)HE.1943-5584.0000525

AbstractThe moments (MOM1 and MOM2), maximum likelihood (ML), sextiles (SEX1 and SEX2) and probability weighted moments (PWM1 and PWM2) methods for estimating the parameters and quantiles of the general extreme value (GEV) distribution for the maxima were analyzed and compared by using data generation techniques of the type of distribution sampling experiments. Considering variance, bias, and mean square error criteria of estimates of parameters and quantiles, it is concluded that in general for the sample sizes analyzed 9≤N≤99 and nonexceedance probabilities in the range 0.90≤F≤0.99, the ML method is superior to the other six. However, the simpler methods may be as good depending on the sample size. The PWM2 is a good option to estimate the location and shape parameter, while MOM1 and MOM2 are an alternative when estimating the shape parameter. Thus, for estimating quantiles for N≤19 the MOM1, MOM2, and PWM2 method compares quite well with the ML method, while for N>19 the PWM2 shows a better performance. When compared with ML, the PWM2 method showed an overall better performance in estimating the quantiles for large negative values of the shape parameter and for small sample sizes.