TRANSFORMATION AND NORMALIZATION OF VARIATES WITH SPECIFIED DISTRIBUTIONS

Given two continuous random variables X and Y, with specified strictly increasing cumulative distribution functions F and G, respectively, t he one to-one transform t which maps one variate into another, say Y = t(X), has an analytic form, t(X) = G(-1)(F(X)) or t(X) = G(-1)(1 - F( X)), depending upon whether t is increasing or decreasing. This fact o f probability theory is reviewed and compared with another method for finding t that was recently proposed. Applications to system identific ation, normalization of a variate, and normalization of a sample are b riefly discussed. (C) 1997 Elsevier Science B.V.