Lepage test

In statistics, the Lepage test is an exact distribution-free test for jointly monitoring the location and scale (variability) in two-sample treatment versus control comparisons. It is a rank test for the two-sample location-scale problem. The Lepage test statistic is the squared Euclidean distance of the standardized Wilcoxon rank-sum test for location and the standardized Ansari–Bradley test for scale. The Lepage test was first introduced by Yves Lepage in 1971 in a paper in Biometrika. A large number of Lepage-type tests exists in statistical literature for simultaneously testing location and scale shifts in case-control studies. The details may be found in the book: Nonparametric statistical tests: A computational approach. Wolfgang Kössler in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions. Amitava Mukherjee and Marco Marozzi introduced a class of percentile modified versions of the Lepage test. An alternative to the Lepage-type tests is known as the Cucconi test proposed by Odoardo Cucconi in 1968.

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