On characterization of multivariate stable distributions via random linear statistics

Abstract

LetX1,X2, ...,Xn be independent and identically distributed random vectors inRd, and letY=(Y1,Y2, ...,Yn)′ be a random coefficient vector inRn, independent ofXj/′. We characterize the multivariate stable distributions by considering the independence of the random linear statistic $$U = Y_1 X_1 + Y_2 X_2 + \cdot \cdot \cdot + Y_n X_n $$ and the random coefficient vectorY.