ORDERING PROPERTIES OF SPACINGS FROM HETEROGENEOUS GEOMETRIC SAMPLES
ORDERING PROPERTIES OF SPACINGS FROM HETEROGENEOUS GEOMETRIC SAMPLES
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DOI：
10.1017/s0269964817000134
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发表时间：
2017-05
影响因子：
1.1
通讯作者：
Weiyong Ding;Yiying Zhang;P. Zhao
中科院分区：
文献类型：
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作者：
Weiyong Ding;Yiying Zhang;P. Zhao
在可靠性方面，当通过完成的操作或行程周期数来测量某些设备和组件的寿命时，或者在定期监测连续数据的情况下，几何分布是对某些设备和组件的寿命进行建模的自然选择。本文旨在研究参数之间的异质性如何影响独立异质几何随机变量产生的间距分布和风险率函数等特征。首先，为异质几何样本的第二间距和样本范围提供了分布函数的精细表示。其次，在通常的随机和风险率排序的意义上，对两组独立且异质的几何随机变量的第二间距和样本范围进行随机比较。该成果不仅填补了异构几何样本间距随机特性研究的空白，而且有望在统计和可靠性领域得到应用。
In the reliability context, the geometric distribution is a natural choice to model the lifetimes of some equipment and components when they are measured by the number of completed cycles of operation or strokes, or in case of periodic monitoring of continuous data. This paper aims at investigating how the heterogeneity among the parameters affects some characteristics such as the distribution and hazard rate functions of spacings arising from independent heterogeneous geometric random variables. First, refined representations of the distribution functions are provided for both the second spacing and sample range from heterogeneous geometric sample. Second, stochastic comparisons are carried out on the second spacings and sample ranges for two sets of independent and heterogeneous geometric random variables in the sense of the usual stochastic and hazard rate orderings. The results established here not only fill the gap on the study of stochastic properties of spacings from heterogeneous geometric samples, but also are expected to be applied in the fields of statistics and reliability.