The multi-aspect tests in the presence of ties

Abstract

The two-sample problem is one of the most important topics in various fields, such as biomedical experiments and product quality maintenance. The Lepage-type test, which is the sum of squares of standardized linear rank statistics, has often been used in the location-scale shift model. Recently, the Lepage-type test has been applied to the joint location-scale and joint location-scale-shape problems. In this study, the test statistics based on the Euclidean distance and Mahalanobis distance of standardized linear rank statistics are considered in the presence of ties. The moments of these test statistics are calculated by deriving the moment-generating function of the vector of linear rank statistics. Moreover, the gamma approximation based on these moments is compared with the chi-square approximation based on the limiting null distribution. Simulation studies and data examples demonstrate the usefulness of gamma approximation in the case of small sample sizes.