Some partial orderings of exchangeable random variables by positive dependence

Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such partial orderings are then discussed. Particular examples include ordering multivariate normal, t, [chi]2, Cauchy, exponential, binomial, Poisson, gamma and Farlie-Gumbel-Morgenstern random vectors. Applications to genetic selection and choice of sampling procedures are given.