Covariance matrices associated to general moments of a random vector

It turns out that there exist general covariance matrices associated not only to a random vector itself but also to its general moments. In this paper we introduce and characterize general covariance matrices of a random vector that are associated to some important general moments, which are determined by a specific class of convex functions. As special cases, the original covariance matrices of a random vector, as well as the pth covariance matrices characterized recently, are included. The covariance matrices associated to the p-power function distribution and the logistic distribution are characterized as by-products.