NBUC性的偏序刻画

Characterize property of NBUC by means of partial ordering

为刻画同一类寿命分布中两个不同分布的NBUC性的强弱,本文定义了一个新的偏序,即NBUC序.并证明NBUC序具有反身性、反对称性和传递性.另外,该偏序与凸序、超可加序、NBUE序的关系也作了调查.同时还建立NBUC序在被比较的分布是指数分布情况下的一个充要条件.

In order to characterize the property of NBUC between two distinct lifetime distributions that belong to same class, a new partial ordering named NBUC ordering is defined in this article. We show that NBUC ordering possess reflexivity, anti-symmetry and transitivity. We also survey the relationships between this new ordering and other stochastic ordering, such as convex ordering, super-additive ordering and NBUE ordering. In addition, a sufficient and necessary condition of NBUC ordering is built when compared distribution is exponential.