An asymptotically distribution freetest for assessing the separationbetween two distributions

Abstract

We present a class of asymptotically distribution free tests for the equality of selected quantiles of two continuous distributions F and G based on independent random samples summarized by their empirical distribution functions, denoted [Fcirc] and Ĝ. Our test statistics are based on [Fcirc] evaluated at a quantile of the distribution function H defined as the weighted average Ĥ = b[Fcirc] + (l - b)Ĝ, 0≤b<1. The choice b = 0 yields the control quantile test studied by Chakraborti [4] and others. Inversion of the test statistic defined by b = 0.5 leads to a measure of the separation between F and G. We investigate and compare the performance of some of these tests and a normal theory test proposed by Perng et al. [12] via simulation.

Keywords:

• Equality of quantiles
• separation between distributions
• Behrens-Fisher problem