%0 Journal Article
%T ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
%A Eric Clarkson
%A J. L. Denny
%A Larry Shepp
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/08-AAP536
%X For independent $X$ and $Y$ in the inequality $P(X\leq Y+\mu)$, we give sharp lower bounds for unimodal distributions having finite variance, and sharp upper bounds assuming symmetric densities bounded by a finite constant. The lower bounds depend on a result of Dubins about extreme points and the upper bounds depend on a symmetric rearrangement theorem of F. Riesz. The inequality was motivated by medical imaging: find bounds on the area under the Receiver Operating Characteristic curve (ROC).
%U http://arxiv.org/abs/0903.0518v1