First-order dominance: stronger characterization and a bivariate checking algorithm

How to determine whether one distribution first-order dominates another is a fundamental problem that has many applications in economics, finance, probability theory, and statistics. Nevertheless, little is known about how to efficiently check first-order dominance for finite multivariate distributions. Utilizing that this problem can be formulated as a transportation problem with a special structure, we provide a stronger characterization of multivariate first-order dominance and develop a linear time complexity checking algorithm for the bivariate case. We illustrate the use of the checking algorithm when numerically assessing first-order dominance among continuous bivariate distributions.