Conditional limits of scale mixture distributions

In this paper we introduce the class of W p scale mixture random vectors with a particular radial decomposition and an independent-splitting property specified by some random variable W p , p ∈ ( 0 , ∞ ) . We derive several conditional limit results assuming that the distribution of the random radius is in the max-domain of attraction of a univariate extreme value distribution and W p has a certain tail asymptotic behaviour. As an application we obtain the joint asymptotic distribution of concomitants of order statics considering certain bivariate W p scale mixture random samples.