We propose a new measure of variability in the tail of a distribution by applying a Box–Cox transformation of parameter \(p \ge 0\) to the tail-Gini functional. It is shown that the so-called Box–Cox Tail Gini Variability measure is a valid variability measure whose condition of existence may be as weak as necessary thanks to the tuning parameter p. The tail behaviour of the measure is investigated under a general extreme-value condition on the distribution tail. We then show how to estimate the Box–Cox Tail Gini Variability measure within the range of the data. These methods provide us with basic estimators that are then extrapolated using the extreme-value assumption to estimate the variability in the very far tails. The finite sample behaviour of the estimators is illustrated both on simulated and real data.

通过对尾基尼函数应用参数\（p \ ge 0 \）的Box-Cox变换，我们提出了一种分布尾部变异性的新度量 。结果表明，所谓的“ Box-Cox尾巴基尼变异性”度量是一种有效的变异性度量，由于调整参数p的存在，其存在条件可能会尽可能弱。。在分布尾部的一般极值条件下研究度量的尾部行为。然后，我们展示了如何在数据范围内估计Box-Cox尾巴Gini变异性度量。这些方法为我们提供了基本的估计量，然后使用极值假设对其进行外推，以估计极远尾部的变化。估计器的有限样本行为在模拟数据和实际数据上均得到了说明。