The Lilliefors normality test is a classical extension of the Kolmogorov–Smirnov goodness-of-fit test tailored to assessing normality. A recent modification improves its robustness to outliers by introducing a subsetting function. In this paper, we propose an alternative approach that replaces subsetting functions with Ordered Weighted Averaging (OWA) functions and further generalizes the test to any location-scale family, not only the normal distribution. We conduct extensive experiments on the power of the resulting test for three representative location-scale families—normal, uniform and shifted-exponential—using different weight vectors to define the OWA functions. The results indicate that the best trade-off between robustness and statistical power is achieved by a well-known special class of OWA functions: the order statistics.
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Marina Iturrate-Bobes
Raúl Pérez-Fernández
Bernard De Baets
Fuzzy Sets and Systems
Ghent University
Universidad de Oviedo
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Iturrate-Bobes et al. (Wed,) studied this question.
www.synapsesocial.com/papers/69d892d16c1944d70ce03fdf — DOI: https://doi.org/10.1016/j.fss.2026.109893