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  • https://doi.org/10.1080/03610926.2025.2528366Copy DOI Icon

An improved Lepage-type test statistic for the location-scale problem

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Abstract

In hypothesis testing, it is common to observe a shift in both location and scale simultaneously. Location-scale tests are designed to handle such situations, and combining location and scale test statistics is a popular approach among statisticians. Lepage proposed a combination of the Wilcoxon and Ansari-Bradley tests, respectively, for location-shift and scale-shift alternatives, which is effective for distributions with medium tails and symmetric shapes. To improve power, we replace the standard ranks with recently proposed relative ranks in the Wilcoxon test within the frame of Lepage’s statistic. This modification enhances power for a wider range of distributions, including symmetric, asymmetric, short-tailed, medium-tailed, and long-tailed densities. We conducted Monte Carlo simulations to compare the power performance of our suggested test to the classical Lepage test and another location-scale Cucconi test across various continuous distributions. Our results indicate that the proposed test offers significantly higher power and a more stable significance level, making it a strong contender among location-scale tests. To further illustrate the practical application of our test, we analyzed four real-world biomedical datasets. These examples demonstrate that the suggested test provides a reliable solution for the two-sample independent location-scale testing problem.

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