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Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation

by M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 77 - Number 4
Year of Publication: 2013
Authors: M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer
10.5120/13384-1000

M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer . Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation. International Journal of Computer Applications. 77, 4 ( September 2013), 31-37. DOI=10.5120/13384-1000

@article{ 10.5120/13384-1000,
author = { M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer },
title = { Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation },
journal = { International Journal of Computer Applications },
issue_date = { September 2013 },
volume = { 77 },
number = { 4 },
month = { September },
year = { 2013 },
issn = { 0975-8887 },
pages = { 31-37 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume77/number4/13384-1000/ },
doi = { 10.5120/13384-1000 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:49:23.879386+05:30
%A M. A. W. Mahmoud
%A A. A. Soliman
%A A. H. Abd Ellah
%A R. M. El-sagheer
%T Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation
%J International Journal of Computer Applications
%@ 0975-8887
%V 77
%N 4
%P 31-37
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The coefficient of variation (CV ) of a population is defined as the ratio of the population standard deviation to the population mean. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on the upper record values, we study the behavior of the CV of a random variable that follows a Lomax distribution. Specifically, we compute the maximum likelihood estimations (MLEs) and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo (MCMC) techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on a real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.

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Index Terms

Computer Science
Information Sciences

Keywords

Lomax distribution Coefficient of variation Markov chain Monte Carlo Upper record value Bootstrap

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