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

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.