Motivated by upper-tail quantile-domain summaries, we study the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. We derive statistical properties of this measure and consider a rational (Möbius) specification of the quantilebased effectiveness persistence function. Under natural boundary conditions, this specification reduces to a canonical form. The resulting canonical family defines a two-parameter class of nonnegative distributions through its quantile function. Various properties, including descriptive measures, L-moments, and quantile-based reliability concepts, are derived for this class. Estimation of the model parameters using maximum likelihood is also developed. The proposed family is illustrated using a real survival dataset.

翻译：受上尾分位数域汇总的启发，我们研究了基于分位数的疗效持久性函数，该函数定义为尾部均值与分位数函数之比。我们推导了该测度的统计性质，并考虑了基于分位数的疗效持久性函数的有理（莫比乌斯）规范形式。在自然边界条件下，该规范形式简化为标准形式。由此得到的标准族通过其分位数函数定义了一个双参数非负分布类。我们推导了该类分布的各种性质，包括描述性测度、L矩和基于分位数的可靠性概念。同时发展了利用最大似然法估计模型参数的方法。最后通过一个实际生存数据集对所提出的分布族进行了说明。