International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 407-408

Separation metrics for real-valued random variables

Michael D. Taylor

Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 3 April 1984

Copyright © 1984 Michael D. Taylor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


If W is a fixed, real-valued random variable, then there are simple and easily satisfied conditions under which the function dW, where dW(X,Y)= the probability that W “separates” the real-valued random variables X and Y, turns out to be a metric. The observation was suggested by work done in [1].