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Assume that two independent random samples are distributed according to a log-logistic distribution (LLD). In this study, the score functions for the locally most powerful rank test were derived for the location and scale parameters. The Wilcoxon rank-sum test was shown to be locally most powerful rank test for the LLD. The asymptotic efficiency of the Wilcoxon rank-sum test was derived and compared with that of the modified Wilcoxon rank-sum test for the LLD.

Asymptotic efficiency and small sample power of a locally most powerful linear rank test for the log-logistic distribution