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The null and non-null limiting distributions of the modified multisample Cucconi test

ABSTRACT Various test statistics have been proposed to address the two-sample location-scale problem. A nonparametric one-way layout analysis of variance plays an important role in biometry. We consider a multisample nonparametric statistic for the location-scale problem. The multisample Cucconi test is suitable for the shifted location-scale parameter. However, the limiting distribution of the multisample Cucconi test has not been derived prior to this publication. The null and non-null limiting distribution of the modified multisample Cucconi test is derived. Simulation studies are used to investigate the convergence of the multisample Cucconi test to the limiting distribution under various scenarios.