Rates of convergence of powered order statistics from general error distribution

Abstract

Let be a sequence of independent random variables with common general error distribution with shape parameter v>0, and let denote the r-th largest order statistics of . With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.