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Research Paper | Mathematics and Statistics | Mexico | Volume 13 Issue 4, April 2024

Estimation of a Measure of Skewness Taking the Median as the Axis of Symmetry

Jose Moral de la Rubia

Abstract: Skewness is a property defining the shape of a distribution, with various methods available for its measurement. A recent proposal by Gunver, Senocak, and Vehid, denoted as gGSV, utilizes the median as the axis of symmetry. The first objective of this article is to develop a script for point and interval estimation of gGSV using the R program. Bootstrap confidence intervals are computed using percentile and bias-corrected and accelerated percentile methods. The script also includes skewness evaluation through bootstrap probability and visual examination of distribution via a box plot and histogram. To illustrate, the script is applied to a random sample conforming to a logistic distribution. The second objective is to establish interpretive symmetry rules for gGSV, accomplished by generating bootstrap confidence intervals at 90%, 95%, and 99% from 34 population-samples of various sizes following a standard normal distribution. A third objective is to analyze the relationship of gGSV with quartile and percentile skewness coefficients, and jackknife acceleration. It is concluded that gGSV can be interchanged with the percentile skewness coefficient. Moreover, if variable X adheres to a normal distribution or satisfies the conditions of the central limit theorem, the sampling distribution of gGSV(x) converges to normality.

Keywords: shape measure, skewness, confidence interval, bootstrap, R program

Edition: Volume 13 Issue 4, April 2024,

Pages: 937 - 949