Conditional Limits of L_p scale Mixture Distributions

In this paper we introduce the class of L_p random vectors which includes beta-independent random vectors and L_p Dirichlet ones. We derive several conditional limit results assuming that the associated random radius of the L_p random vectors have distribution function in the max-domain of attraction of a univariate extreme value distribution function. As an application we obtain the joint asymptotic distribution of concomitants of order statics considering L_p random samples.