Positive dependence of random variables with a common marginal distribution
In this paper we review some notions of positive dependence of random variables with a common univariate marginal distribution and describe the related moment and probability inequalities. We first present a comparison between i.i.d. random variables and exchangeable random variables via an application of de Finetti's theorem, then describe some useful probability inequalities via partial orderings of the strength of their positive dependence. Finally, we state a result for random variables which are not necessarily exchangeable. Special applications to the multivariate normal distribution will be discussed, and the results involve only the correlation matrix of the distribution.