Conditional limits of Wp scale mixture distributions

In this paper we introduce the class of Wp scale mixture random vectors with a particular radial decomposition and an independent-splitting property specified by some random variable Wp,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 Wp has a certain tail asymptotic behaviour. As an application we obtain the joint asymptotic distribution of concomitants of order statics considering certain bivariate Wp scale mixture random samples.