科研之友
微信
新浪微博
Facebook
分享链接
摘要
Consider the problem of drawing random variates (X-1, . . ., X-n) from a distribution where the marginal of each X-i is specified, as well as the correlation between every pair X-i and X-j. For given marginals, the Frechet-Hoeffding bounds put a lower and upper bound on the correlation between X-i and X-j. Any achievable correlation between X-i and X-j is a convex combination of these bounds. We call the value lambda(X-i, X-j) is an element of [0, 1] of this convex combination the convexity parameter of (X-i, X-j) with lambda(X-i, X-j) = 1 corresponding to the upper bound and maximal correlation. For given marginal distributions functions, F-1, . . ., F-n of (X-1, . . ., X-n), we show that lambda(X-i, X-j) = lambda(ij) if and only if there exist symmetric Bernoulli random variables. (B-1, . . ., B-n) (that is {0,1} random variables with mean 1/2) such that lambda(B-i, B-j) = lambda(ij). In addition, we characterize completely the set of convexity parameters for symmetric Bernoulli marginals in two, three, and four dimensions.
- 出版日期2015-6
