Conditional Limits of W_p scale Mixture Distributions

TL;DR

This paper introduces W_p scale mixture distributions with a specific radial structure, deriving their conditional limits under extreme value conditions, and applies these results to analyze joint asymptotics of order statistics.

Contribution

It defines a new class of W_p scale mixture distributions and establishes their conditional limit behavior under extreme value assumptions, with applications to order statistics.

Findings

Derived conditional limit results for W_p scale mixtures.

Established asymptotic distribution of concomitants of order statistics.

Provided a framework for analyzing extreme behavior in mixture models.

Abstract

In this paper we introduce the class of W_p scale mixture random vectors with a particular radial decomposition and a independent splitting property specified by some random variable W_p, and a positive constant p. 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 miture samples.