Goodness-of-fit Test for Extreme Value Type I Distribution

Abstract

This study investigates the properties of goodness-of-fit test using the Kolmogorov-Smirnov (KS), Cramer-von Mises (CM), Anderson Darling (AD), Watson (W) and probability plot correlation coefficient (R) statistics for goodness-of-fit test for extreme value type-1 (EV1) distribution. The parameters of EV1 are estimated by the L-moment (LMOM), moment (MOM) and least-square (LS) method. For each test, Monte Carlo techniques are used to generate critical values for sample sizes 5(5)50 and 50(10)100. The power of the goodness-of-fit tests are investigated under General Extreme Value (GEV) distribution. The power comparison shows that the LS is combined with the symmetrical rank gives more powerful results than LMOM and MOM for all statistics. Our study shows that the AD statistic is most powerful among the methods and is recommended for future study. Keywords: Kolmogorov-Smirnov (K-S); Cramer-von Mises (C-M); Anderson-Darling; Watson (W) and correlation coefficient (R); Extreme-Value Type-1, L-Moment