A New Distribution-Free Test Based on Order Statistics

We propose a new distribution-free, nonparametric test to evaluate the equality of two continuous distributions based on order statistics. In the test statistic, we use the precedence and the exceedance statistics. Its exact finite sample distribution as well as its asymptotic distribution under the null hypothesis are derived. Some simulation studies indicate good power properties of the proposed test against classical nonparametric tests, especially under scale and tail differences.