New Measures of Skewness of a Probability Distribution

Abstract

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 ob- tained 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).