Precedence tests and Lehmann alternatives

Abstract

Precedence tests are considered in the context of four classes of one-sided Lehmann-type alternatives: G = K ^k (k > 1); G = 1 - (1-F)^k (k < 1); G = F ^k (k < 1); and G = 1 - (1-F)^k (k > 1), where F and G are two continuous cumulative distribution functions. If an optimal precedence test (one with the maximal power) is determined for one of these four classes, the optimal tests for the other classes of alternatives can be derived. Application of this is given using the results of Lin and Sukhatme (1992) who derived the best precedence test for testing the null hypothesis that the lifetimes of two types of items on test have the same distribution. The test has maximum power for fixed k in the class of alternatives G = 1-(1-F)^k (, with k < 1. Best precedence tests for the other three classes of Lehmann-type alternatives are derived using their results. Finally, a comparison of precedence tests with Wilcoxon’s twosample test is presented.