ABSTRACT
Let X1, . . . , Xn1 be a random sample with common distribution function F (x) and density function f(x). Let Y1, . . . , Yn2 be another random sample, independent of the first, with common distribution function G(x) and density g(x). We call this the general model throughout this chapter. A natural null hypothesis is H0 : F (x) = G(x). In this chapter we consider rank and sign tests of this hypothesis. A general alternative to H0 is HA : F (x) 6= G(x) for some x. Except for Section 2.10 on the scale model we are generally concerned with the alternative models where one distribution is stochastically larger than the other; for example, the alternative that G is stochastically larger than F which can be expressed as HA : G(x) ≤ F (x) with a strict inequality for some x. This family of alternatives includes the location model, described next, and the Lehmann alternative models discussed in Section 2.7, which are used in survival analysis.
