Volume 4, Issue 4, December 2018, Page: 68-73
An Empirical Examination of the Asymptotic Normality of the kth Order Statistic
Mbanefo Solomon Madukaife, Department of Statistics, University of Nigeria, Nsukka, Nigeria
Received: Oct. 29, 2018;       Accepted: Nov. 15, 2018;       Published: Jan. 29, 2019
DOI: 10.11648/j.ijsd.20180404.11      View  157      Downloads  37
Abstract
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.
Keywords
Asymptotic Normality, Inverse Distribution Function, kth Order Statistic, Monte Carlo Simulation, pth Quantile, Test for Normality
To cite this article
Mbanefo Solomon Madukaife, An Empirical Examination of the Asymptotic Normality of the kth Order Statistic, International Journal of Statistical Distributions and Applications. Vol. 4, No. 4, 2018, pp. 68-73. doi: 10.11648/j.ijsd.20180404.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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