Abstract

In [1], the authors introduced the geometric vitality function that explains the failure pattern of components or systems based on the geometric mean of the remaining lifetime. Recently, studies based on quantile function played an essential role in the research domain because of its unique properties than the distribution function method. Based on this, we define geometric vitality function in terms of quantile function and established monotone, ordering properties for the proposed measure. In addition to this, we also introduce the proposed measure in the context of order statistics. Some important properties were discussed for the proposed measure. Finally, we provide an application of the new measure for some distributions useful in lifetime data analysis.

中文翻译：

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基于分位数的订单统计几何活力函数

摘要

在 [1] 中，作者引入了几何活力函数，该函数基于剩余寿命的几何平均值来解释组件或系统的失效模式。最近，基于分位数函数的研究因其比分布函数方法独特的性质在研究领域发挥了重要作用。基于此，我们根据分位数函数定义几何活力函数，并为所提出的度量建立单调、有序的属性。除此之外，我们还在订单统计的背景下介绍了建议的措施。讨论了所提议措施的一些重要特性。最后，我们提供了新度量在生命周期数据分析中有用的一些分布的应用。