Second order Expansions for Extreme Quantiles of Burr Distributions and Asymptotic Theory of Record Values

TL;DR

This paper develops second order expansions for extreme quantiles of Burr distributions and applies these to analyze record values, leading to new statistical tests in extreme value theory.

Contribution

It provides novel second order quantile expansions for Burr distributions and uses them to characterize record value asymptotics and develop new statistical tests.

Findings

Derived second order quantile expansions for Burr distributions.

Characterized asymptotic laws of record values for Burr distributions.

Proposed new statistical tests based on these asymptotic laws.

Abstract

In this paper we investigate the Burr distributions family which contains twelve members. Second order expansions of quantiles of the Burr's distributions are provided on which may be based statistical methods, in particular in extreme value theory. Beyond the proper interest of these expansions, we apply them to characterize the asymptotic laws of their records of Burr's distributions, lead to new statistical tests.