A NONPARAMETRIC TEST OF SYMMETRY VERSUS ASYMMETRY FOR RANKED-SET SAMPLES

Abstract

This paper introduces a nonparametric test of symmetry for ranked-set samples to test the asymmetry of the underlying distribution. The test statistic is constructed from the Cramér-von Mises distance function which measures the distance between two probability models. The null distribution of the test statistic is established by constructing symmetric bootstrap samples from a given ranked-set sample. It is shown that the type I error probabilities are stable across all practical symmetric distributions and the test has high power for asymmetric distributions.

Keywords:

• Bootstrap distribution
• Cramer-von Mises distance
• Design
• Hodges-Lehmann estimator
• Median
• Mode
• Unequal allocation
• Mathematics Subject Classification Codes (1991): 62G30; 62H10

ACKNOWLEDGMENT

The author thanks to the anonymous referee for his/her helpful comments and suggestions.