Goodness-of-fit Tests for the Type-I Extreme-value and Two-parameter Weibull Distributions with Unknown Parameters Estimated by Graphical Plotting Techniques

Résumé du livre

The objective of this study is to determine the critcal values of the Cramer-von Mises (C-M) and Anderson-Darling (A-D) statistics for goodness-of-fit tests for the Type-I extreme-value and two-parameter Weibull distributions when the population parameters are estimated from a complete sample by grapical plotting techniques. Three kinds of graphical plotting technique, i.e., the median ranks, mean ranks, and symmetrical sample cumulative distribution (symmetrical ranks), are combined with the least-squares method on extreme-value and Weibull probability paper to estimate the parameters. Monte Carlo simulation is used to calculate the critcal values of the C-M and A-D statistics, in which 1,000,000 sets of complete samples are generated ten times for each sample size of 3(1)20, 25(5)50, and 60(10)100. The critical values are discussed and tabulated for practical use.