If your Spearman's correlation matrix is positive semi-definite, you can always construct a joint distribution with those correlations and your specified marginals.
Check out the theory of Copulas. Copulas are the jointly uniform multivariate distributions which characterize the dependence relationships in every multivariate distribution. Essentially every joint distribution can be identified uniquely by its copula and its marginals (Sklar's Theorem). A very good first reference is Nelsen's "An Introduction to Copulas," This book is volume 139 in Springer's "Lecture Notes in Statistics." Have fun with copulas. [EMAIL PROTECTED] (Ralph Lorentzen) writes: > > I'm new to this group, so my question may have been answered earlier. > > Suppose we know all marginal distributions of n random variables. > There are of > course in general many joint distributions which have these marginal > distributions, (We may for instance multiply the marginal > distributions if we assume independence.) I want to narrow down the > choice by specifying all > covariances. It is easy to see that I cannot choose any set of > covariances even if I secure that the variance/covariance matrix to be > positive semidefinite. Is there a set of conditions on the covariances > which guarantees that a joint distribution exists? -- George MacKenzie Multivariate Models R&D SAS . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
