Goodness-of-fit tests for type-I extreme-value and 2-parameterWeibull distributions

摘要

This study investigates the properties of the Kolmogorov-Smirnovn(K-S), Cramer-von Mises (C-M) and Anderson-Darling (A-D) statistics forngoodness-of-fit tests for type-I extreme-value and for 2-parameternWeibull distributions, when the population parameters are estimated fromna complete sample by graphical plotting techniques (GPT). ThreenGPT-median ranks, mean ranks, symmetrical sample cumulative distributionn(symmetrical ranks)-are combined with the least-squares method (LSM) onnextreme-value and Weibull probability paper to estimate the populationnparameters. The critical values of the K-S, C-M, A-D statistics arencalculated by Monte Carlo simulation, in which 106 sets ofnsamples for each sample size of 3(1)20, 25(5)50, and 60(10)100 arengenerated. The power of the K-S, C-M, A-D statistics are investigatednfor 3 graphical plotting techniques and for maximum likelihoodnestimators (MLE). A Monte Carlo simulation provided the power resultsnusing 104 repetitions for each sample size of 5, 10, 25, 40.nThe power comparison showed that: Among 3 GPT, the symmetrical ranksngive more powerful results than the median and mean ranks for the K-S,nC-M, A-D statistics; Among 3 GPT and the MLE, the symmetrical ranksnprovide more powerful results than the MLE for the K-S and A-Dnstatistics; for the C-M statistic, the MLE provide more powerful resultsnthan 3 GPT; Generally, the A-D statistic coupled with the symmetricalnranks and LSM is most powerful among the competitors in this study andnis recommended for practical use