The generalized multisample Cucconi test statistic for the location and scale parameters

Abstract

Many researchers study various test statistics for appropriately dealing with data. The nonparametric one-way analysis of variance plays an important role in biometry. For the multisample location-scale problem, the generalized Cucconi test statistic has been proposed for the location, scale, and location-scale parameters. This study derives the limiting distribution of the suggested test statistic. Computing the exact critical value of the statistic can be difficult when the sample sizes are large. An approximation method regarding the distribution function of the test statistic can be useful in this situation. We use a gamma approximation to evaluate the upper-tail probability of the proposed test statistic for a finite sample size.