The joint probability density function \(f\) of two random variables \(X\) and \(Y\) satisfies, for every \(a_1 b_1\) and \(a_2 b_2\), \[ P(a_1\le X\le b_1, a_2\le Y ...

We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two ...