TITLE:
New Measures of Skewness of a Probability Distribution
AUTHORS:
Ashok K. Singh, Laxmi P. Gewali, Jiwan Khatiwada
KEYWORDS:
Sample Moments, Quantiles, Computational Geometry, Symmetry, Robust Measure, Central Limit Theorem, Trapezoid Rule
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.5,
October
31,
2019
ABSTRACT: Symmetry of the underlying probability density plays an
important role in statistical inference, since the sampling distribution of the sample mean for a given sample size is more likely to be approximately normal for a
symmetric distribution than for an asymmetric one. In this article, two new
measures of skewness are proposed and the confidence intervals for true
skewness are obtained via Monte Carlo simulation experiments. One advantage of
the two proposed skewness measures over the standard measures of skewness is
that the proposed measures of skewness take values inside the range (-1, +1).