The Eaton problem and multiplicative properties of multivariate distributions

A new representation is proposed for the scale factor (so-called standard) in the Eaton problem on n-dimensional versions of random vectors. An extension of the Eaton problem to the nonsymmetric case is formulated. A new approach based on analysis of multiplicative properties of random vectors and random variables is suggested, which permits, in particular, to establish, with uniformity of attitude, most of the presently known results on description of classes of n-dimensional versions.