Enhanced Lepage-type test statistic for location-scale shifts with right-skewed data

The two-sample location-scale problem is a frequent challenge in statistical inference, particularly in fields like biomedicine where data are often right-skewed. While the classical Lepage test offers a standard nonparametric solution, its sensitivity to right-skewed data can limit its power in practice. This study proposes an enhanced Lepage-type test statistic that addresses these limitations by integrating two modern robust components: the Fong-Huang variance estimator for the location component and a novel empirical-based variance estimator for the Ansari-Bradley scale component. This new estimator provides a unified, unbiased, and consistent estimator for the variance of the Ansari-Bradley statistic. Extensive Monte Carlo simulations across six common right-skewed distributions (exponential, gamma, chi-square, lognormal, Weibull, and half-Cauchy) demonstrate that the proposed test achieves a consistent and meaningful power advantage over the classical Cucconi and Lepage tests while maintaining strict Type I error control at the nominal level. The practical utility of the new statistic is confirmed through analyses of four real-world biomedical datasets, providing practitioners with a more powerful and reliable tool for analyzing right-skewed data. To facilitate adoption, we provide implementation guidance and an accompanying R code.