Distribution-Free Two-Sample Tests Based on Rank Spacings

Abstract

For the two-sample problem, rank spacings of one sample are the positive integer distances between combined-sample ordered ranks from that sample. Elementary mathematical development yields distribution-free orthogonal components analogous to L statistics used by Kaigh for assessing one-sample uniformity. Rank spacings components are linear combinations of ordered ranks with Hahn polynomial vector weight functions. The first four rank spacings components provide nonparametric measures of location, scale, skewness, and kurtosis. Asymptotically normal rank spacings components are related to linear rank statistic components obtained by Pettitt. Aggregates of squared rank spacings components yield a component decomposition of the Dixon statistic and provide omnibus chi-squared statistics analogous to those of Pettitt and Boos.

Key Words:

• Exceedance statistic
• L moment
• Orthogonal components
• O statistic
• Spacing