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.
| Published in | International Journal of Statistical Distributions and Applications (Volume 4, Issue 4) |
| DOI | 10.11648/j.ijsd.20180404.11 |
| Page(s) | 68-73 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Asymptotic Normality, Inverse Distribution Function, kth Order Statistic, Monte Carlo Simulation, pth Quantile, Test for Normality
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APA Style
Mbanefo Solomon Madukaife. (2019). An Empirical Examination of the Asymptotic Normality of the kth Order Statistic. International Journal of Statistical Distributions and Applications, 4(4), 68-73. https://doi.org/10.11648/j.ijsd.20180404.11
ACS Style
Mbanefo Solomon Madukaife. An Empirical Examination of the Asymptotic Normality of the kth Order Statistic. Int. J. Stat. Distrib. Appl. 2019, 4(4), 68-73. doi: 10.11648/j.ijsd.20180404.11
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Download@article{10.11648/j.ijsd.20180404.11,
author = {Mbanefo Solomon Madukaife},
title = {An Empirical Examination of the Asymptotic Normality of the kth Order Statistic},
journal = {International Journal of Statistical Distributions and Applications},
volume = {4},
number = {4},
pages = {68-73},
doi = {10.11648/j.ijsd.20180404.11},
url = {https://doi.org/10.11648/j.ijsd.20180404.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20180404.11},
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.},
year = {2019}
}
TY - JOUR T1 - An Empirical Examination of the Asymptotic Normality of the kth Order Statistic AU - Mbanefo Solomon Madukaife Y1 - 2019/01/29 PY - 2019 N1 - https://doi.org/10.11648/j.ijsd.20180404.11 DO - 10.11648/j.ijsd.20180404.11 T2 - International Journal of Statistical Distributions and Applications JF - International Journal of Statistical Distributions and Applications JO - International Journal of Statistical Distributions and Applications SP - 68 EP - 73 PB - Science Publishing Group SN - 2472-3509 UR - https://doi.org/10.11648/j.ijsd.20180404.11 AB - 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. VL - 4 IS - 4 ER -
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