Contributions to the Theory of Rank Order Statistics: Applications of Lattice Theory

Introduction. As a typical problem, i~ x 1 , ,xm are the observations in a first sample an~ y 1 , ,yn are the observa~ions in a second sample, then the ranks of the y's in the combined sample is the observed rank order. Thus the observed rank order r will be a vector (r 1 , ,rn) consisting of an ordered subset of the integers l, ,m+n. Correaponding to the observed rank order r is the random variable R. If the x's and y' are identically and independently distributed then for each possibler, one has P(R=r) = (m+n)-1 On the other hand, if the x's are n . a sample from a population with continuous cumulative distribution function F(.)