Recently, expectile-based measures of skewness have been introduced which possess quite promising properties (Eberl and Klar, 2021, 2020). However, it remained unanswered whether these measures preserve the convex transformation order of van Zwet, which is a basic requirement for a measure of skewness. It is one aim of this paper to answer this question in the affirmative. These measures of skewness are scaled using interexpectile distances. We introduce orders of variability based on these quantities and show that the so-called expectile dispersive order is equivalent to the dilation order. Further, we analyze the statistical properties of empirical interexpectile ranges in some detail.

翻译：最近,引入了具有相当有前途的特性的基于预期的扭曲度量(Eberl和Klar,2021年,2020年),然而,对于这些措施是否保留范兹韦特的孔韦克斯变异顺序(这是衡量斜度的一个基本要求),仍没有答案;本文的一个目的是肯定地回答这一问题。这些扭曲度度量是用预期之间的距离来测量的。我们根据这些数量提出变异顺序,并表明所谓的预期分散顺序相当于变异顺序。此外,我们比较详细地分析了实验性跨端范围的统计属性。