Recently, expectile-based measures of skewness akin to well-known quantile-based skewness measures have been introduced, and it has been shown that these measures possess quite promising properties (Eberl and Klar in Comput Stat Data Anal 146:106939, 2020; Scand J Stat, 2021, https://doi.org/10.1111/sjos.12518). However, it remained unanswered whether they preserve the convex transformation order of van Zwet, which is sometimes seen as a basic requirement for a measure of skewness. It is one of the aims of the present work 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 weak expectile dispersive order is equivalent to the dilation order. Further, we analyze the statistical properties of empirical interexpectile ranges in some detail.

最近，引入了类似于众所周知的基于分位数的偏度测量的基于期望的偏度测量，并且已经表明这些测量具有非常有前景的特性（Eberl 和 Klar 在 Comput Stat Data Anal 146:106939, 2020; Scand J 统计，2021，https://doi.org/10.1111/sjos.12518）。然而，它们是否保留 van Zwet 的凸变换顺序仍然没有答案，这有时被视为衡量偏度的基本要求。肯定地回答这个问题是本工作的目的之一。这些偏度的度量是使用互预期距离来衡量的。我们基于这些量引入可变性阶数，并表明所谓的弱预期色散阶数等价于膨胀阶数。更远，