随机序与寿命分布类  

Stochastic Orderings and Classes of Life Distributions

作　　者：邓永录[1] 

机构地区：[1]中山大学数学系,广州510275

出　　处：《运筹学杂志》1995年第2期34-54,共21页

基　　金：国家自然科学基金资助项目

摘　　要：各种各样的随机序是随机比较方法的最基本的概念。每一种新的、有实际背景和理论依据的随机序的引入都会丰富随机比较方法的研究内容,也有可能使人们更好洞察和理解其中某些概念和结果的本质。而反映时效性质的寿命分布类的研究不仅是随机比较方法的重要组成部分,而且它在运筹学、应用概率和统计学中有广泛的应用。各种寿命分布类的定义密切联系于各种不同的随机序,而且人们还可以反过来从寿命分布类出发定义新的随机序,由此又能引入新的寿命分布类。本文拟将近年这两方面的研究内容和结果作一概括的介绍。Various stoshastic orderings are basic concepts and useful tools of the comparison methods for stochastic modols.And varietis of classes of life distributions describing different aging properties are very useful in reliability theory,maitenance theory,applied probability and statistics. Moreover,tochastic orderings and classes of life distributions are related closely.In present paper,we give a survey of the current development of the studies of these two subjects.At first,after introducing a number of definitions of stochastic orderings we discuss the ideas defining stochastic orderings and the closed properties of some orderings under different operations, and give some relationships among these orderings.Secondly,we also discuss the ideas defining classes of life distributions and the closed properties of some ] classes under different operations, and give some relationships among various classed of life distributions.Thirdly,we discuss the relation between stochastic orderings and classes of life distributions,particularly,we point out that some new stochastic orderings can be defined by means of classes of life distributions,and vice versa.

关 键 词：随机序 寿命分布类 时效性质 封闭性质 指数分布 

分 类 号：O211.5[理学—概率论与数理统计] O213.2[理学—数学]