Variability measures are important tools in the construction of premium principles and risk aversions. In this paper, we propose a family of such measures based on a distorted weighted cumulative residual entropy, which follows by a sensitivity analysis of distortion risk measures. For this family, we obtain properties, connections with other measures, a covariance representation, and some useful interpretations. Furthermore, we explore an application on premium principles based on beta generated distributions, and we give an empirical estimation. We also provide bounds and numerical illustrations.

中文翻译：

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基于累积残余熵和畸变函数的一系列变异性测量

变异性指标是构建溢价原则和风险规避的重要工具。在本文中，我们提出了一系列基于扭曲加权累积残余熵的此类度量，随后对扭曲风险度量进行了敏感性分析。对于这个族，我们获得属性、与其他度量的联系、协方差表示和一些有用的解释。此外，我们探索了基于贝塔生成分布的溢价原则的应用，并给出了实证估计。我们还提供边界和数字插图。