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

Hidetoshi Murakami

doi:10.1007/s40096-014-0135-4

Abstract

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.

Highlights

Testing hypotheses is one of the most important problems in performing nonparametric statistics
Because finite sample sizes are used in practice, we investigated a small sample power of the original and modified Wilcoxon rank-sum tests
We considered the locally most powerful rank test (LMPRT) for the location and scale parameters with the log-logistic distribution (LLD)

Summary

Introduction

Testing hypotheses is one of the most important problems in performing nonparametric statistics. Runde [13] derived the score functions of LMPRTs for the location and scale parameters with the Levy distribution. The score function of the LMPRT is derived for the LLD for the location parameter.

Results

Conclusion