Ann-dimensional random vector is said to have an[alpha]-symmetric distribution,[alpha]0, if its characteristic function is of the form[phi]((u1[alpha]+...+un[alpha])1/[alpha]). We study the classes[Phi]n([alpha]) of all admissible functions[phi]: [0, [infinity])--. It is known that members...

Radial positive definite functions are of importance both as the characteristic functions of spherically symmetric probability distributions, and as the correlation functions of isotropic random fields. The Euclid's hat functionhn(||x||),x[set membership, variant]n, is the self-convolution of an...

This article proposes compactly supported correlation functions, which parameterize the smoothness of the associated stationary and isotropic random field. The constructions are straightforward, and compact support is relevant for various ends: computationally efficient spatial prediction, fast...