Estimation of Modified Measure of Skewness

Abstract

It is well known that the classical measures of skewness are not reliable and their sampling distributions are not known for small samples. Therefore, we consider the modified measure of skewness that is defined in terms of cumulative probability function. The main advantage of this measure is that its sampling distribution is derived from sample data as the sum of dependent Bernoulli random variables. Moreover, its variance and confidence interval are obtained based on multiplicative binomial distribution. Comparison with classical measures using simulation and an application to actual data set are given.