Let X = (X1, X2,..., Xn) be a random vector in Rn (Euclidean n-space) with density f(x). X or f(x) is said to be multivariate reverse rule of order 2 (MRR2) if f(x [curly logical or] y) f(x [curly logical and] y) = f(x) f(y) where the lattice operations x [curly logical and] y and x [curly...

A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) = f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2...