An Empirical Examination of the Asymptotic Normality of the kth Order Statistic

摘要

In this paper, the equivalence of the sample pth quantile of a distribution and the kth order statistic of a random sample obtained from the distribution is reviewed. Based on the review, a new corollary on the almost sure convergence of the kth order statistic to the pth quantile was obtained without proof. Through an extensive Monte Carlo simulation, the extreme as well as the central kth order statistics of five different continuous distributions were obtained at different sample sizes and the asymptotic normality of the order statistics were investigated with the use of the Anderson - Darling (AD) statistic for normality test. The result showed among other things that asymptotic normality holds only for the central order statistics.