A continuous metric scaling solution for a random variable

Abstract

As a generalization of the classical metric scaling solution for a finite set of points, a countable set of uncorrelated random variables is obtained from an arbitary continuous random variable X. The properties of these variables allow us to regard them as principal axes for X with respect to the distance function d(u, v) = [formula]. Explicit results are obtained for uniform and negative exponential random variables. © 1995 Academic Press, Inc.