Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of stochastic order by concentration. We give an application to the Beta family of distributions, and specifically to the one-parameter subfamily with constant mean. This leads to using U.S. household income data to fit generalized Beta distributions and offers a new measure of income concentration.

翻译：衡量随机变量的集中程度是概率论与统计学中的基本概念。本文探讨了有界支撑连续随机变量的一类集中性度量，并利用该度量提出了基于集中程度的随机序概念。我们将其应用于Beta分布族，特别关注均值恒定条件下的一参数子族。这一应用促使我们利用美国家庭收入数据拟合广义Beta分布，从而提供了一种新的收入集中度度量方法。