ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
For independent X and Y in the inequality P(X≤Y+μ), 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 …