Indices of Skewness Derived from a Set of Symmetric Quantiles: A Statistical Outline with an Application to National Data of E.U. Countries

In this paper, which follows a recent field of research started by Tukey (1977), a class of indices of skewness is introduced, based on a symmetric set of quantiles. Two kinds of normaisation are proposed, leading to different indices, called VCS (Ventile Coefficient of Skewness) and VIS (Ventile Index of Slewness), respectively. The sample distribution of both indices is studied by a Monte Carlo simulation. Two extended indices of skewness (ECS and EIS) are proposed, having interesting inferential properties. Finally, an application to national data of 27 E.U. countries is presented, with a brief comment of the results. 1 Introducing the problem The most known and successful index of skewness ever proposed is surely Pearson’s γ, defined as the ratio of the third central moment to the cube of standard deviation. However, the most recent research lines about skewness do follow a quantile pattern. Such an approach, having the aim to define robust, efficient and user-friendly indices of shape (skewness and kurtosis) has bee