Total Positivity of the Bivariate Absolute Normal Distribution and the Association of a Bivariate T-Distribution.

摘要

Motivated by needs in simultaneous inference, numerous authors have established inequalities for joint probabilities in terms of marginal probabilities. Typically the underlying random variables are jointly normal, and most of the proofs are of an analytic nature. In this note, the authors obtain stronger results in the bivariated case by using relationships between certain notions of bivariate dependence.