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), Cramervon 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 10(6) 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). Monte Carlo simulation provided the power results using 10(4) repetitions for each sample size of 5, 10, 25, 40. The power comparison showed that: -Among 3 CPT, 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.