K-sample Anderson-darling Tests of Fit, for Continuous and Discrete Cases

Two k-sample versions of the Anderson-Darling (AD) test of fit are proposed and their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k − 1)-fold convolution of the 1-sample AD asymptotic distribution. Monte Carlo simulation is used to investigate the null distribution small sample behavior of the two versions under various degrees of data rounding and sample size imbalances. Tables for carrying out these tests are provided and their usage in combining independent 1or k-sample AD-tests is pointed out. Some key words: Combining tests, Convolution, Empirical processes, Midranks, Pearson Curves, Simulation. May 20, 19861 re-typeset with minor corrections March 26, 2008 F.W. Scholz, Affiliate Professor, Department of Statistics, University of Washington, Seattle, WA 98105. and M.A. Stephens, Professor Emeritus, Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6 Canada K-Sample Anderson-Darling Tests of Fit, for Continuous and Discrete Cases F.W. Scholz and M.A.Stephens Boeing Computer Services, MS 9C-01, Seattle WA 98124-0346, P.O. Box 24346, USA Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada