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

This study investigates the properties of the Kolmogorov-Smirnov (K-S), Cramer-von Mises (C-M) and Anderson-Darling (A-D) statistics for goodness-of-fit tests for type-I extreme-value and for 2-parameter Weibull distributions, when the population parameters are estimated from a complete sample by graphical plotting techniques (GPT). Three GPT-median ranks, mean ranks, symmetrical sample cumulative distribution (symmetrical ranks)-are combined with the least-squares method (LSM) on extreme-value and Weibull probability paper to estimate the population parameters. The critical values of the K-S, C-M, A-D statistics are calculated by Monte Carlo simulation, in which 10⁶ sets of samples for each sample size of 3(1)20, 25(5)50, and 60(10)100 are generated. The power of the K-S, C-M, A-D statistics are investigated for 3 graphical plotting techniques and for maximum likelihood estimators (MLE). A Monte Carlo simulation provided the power results using 10⁴ repetitions for each sample size of 5, 10, 25, 40. The power comparison showed that: Among 3 GPT, the symmetrical ranks give more powerful results than the median and mean ranks for the K-S, C-M, A-D statistics; Among 3 GPT and the MLE, the symmetrical ranks provide more powerful results than the MLE for the K-S and A-D statistics; for the C-M statistic, the MLE provide more powerful results than 3 GPT; Generally, the A-D statistic coupled with the symmetrical ranks and LSM is most powerful among the competitors in this study and is recommended for practical use