Approximate Asymptotic Confidence Interval for the Population Standard Deviation based on the Sample Gini’s Mean Difference

Authors

Moustafa O. A. Abu-Shawiesh, Dept. of Mathematics, Faculty of Science, The Hashemite University, Al-Zarqa, 13115, JordanFollow
Aamir Saghir, Dept. of Mathematics, Mirpur University of Science and Technology, Mirpur-10250, PakistanFollow
B. M. Golam Kibria, Dept. of Mathematics and Statistics, Florida International University, Miami, Florida, USAFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, an approximate asymptotic confidence interval for the population standard deviation (σ) is constructed based on the sample Gini’s Mean Difference (GMD). The estimated Coverage Probability (CP) and the Average Width (AW) of the proposed approximate asymptotic confidence interval were studied by means of a Monte-Carlo simulation under different settings and compared with two-widely used methods, namely the exact method and the Bonnet (2006) method. It appears that the proposed approximate asymptotic confidence interval method based on GMD performing well comparing to the exact method for some selected distributions. Two real-life data examples are analyzed to illustrate the implementation of the several methods which also supported the results of the simulation study to some extent.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/130501

Recommended Citation

O. A. Abu-Shawiesh, Moustafa; Saghir, Aamir; and M. Golam Kibria, B. (2019) "Approximate Asymptotic Confidence Interval for the Population Standard Deviation based on the Sample Gini’s Mean Difference," Applied Mathematics & Information Sciences: Vol. 13: Iss. 5, Article 1.
DOI: http://dx.doi.org/10.18576/amis/130501
Available at: https://digitalcommons.aaru.edu.jo/amis/vol13/iss5/1