Functional characterization of some positively dependent bivariate random vectors

[[abstract]]In this paper, we consider three different notions of positive dependence for a bivariate random vector: (i) total positivity of order 2, (ii) stochastic increasingness and (iii) positive quadrant dependence. By defining three classes of arrangement-increasing functions, we show that these three different notions can be unified by functional inequalities. Using these functional inequalities, we derive the relations between the positively dependent notions (i) and (iii) and their corresponding counterparts in stochastic majorization orderings.[[fileno]]2030162010041[[department]]電機工程學