On non-null distribution of ranks

Abstract

Consider the two-sample testing problem from continuous distributions with distribution functions F and G such that G= Y(F) where is a non-decreasing onto function from (0,1) to (0,1). when it is not the identity mapping is usually called Lehmannfs alternative. An algorithm to derive the distribtuions of some rank order statistics under a general rule ψ(u) is developed.

Keywords:

• Lehmann alternatives
• two-sample non-parametric tests
• recursive computation