几类随机序关系关于随机最大与随机最小的反向封闭性质

研究了右扩展序、TTT序、单调增凸序和单调增凹序分别关于随机最大与随机最小的反向封闭性质, 并讨论了相关年龄概念关于随机最大与随机最小的反向封闭性质.     

推广的相关序及其一些性质

本文考虑相关风险序，首先，把Dhaene和Goovaerts于1996年提出的相关序由二维随机向量推广到了多维随机向量的情况；然后，我们讨论了推广的相关序的一些性质；最后作为推论，我们还得到：由相关序可以推出指数序．     

独立元件组成的n中取k系统剩余寿命的年龄性质

研究了独立元件组成的n中取k系统的剩余寿命长度的年龄性质,该系统在时刻t＜0有n-k个元件失效.对于几类寿命分布元件,讨论了元件仅仅独立的情形下,n中取k个系统剩余寿命的特征.     

关于DMRL序的若干结论（英文）

设X,Y为非负绝对连续随机变量,X,Y分别具有各自的分布函数F_X,G_Y,使得F_X(0)=G_Y(0)=0,右连续的反函数F_X~(-1),G_Y~(-1),与生存函数F_X,G_Y.记X≤_(dmrl)Y,称X在DMRL(递减的平均剩余寿命)序下比Y小,如果函数∫_G_Y~(-1)(p)~∞G_Y(x)dx/∫_F_X~(-1)(p)~∞F_X(x)dx关于p∈(0,1)递增.考察了DMRL序的特征性质,获得了若干封闭与逆封闭性质.同时,给出了满足DMRL序的若干说明性实例.     

LIR序关系的一些封闭性质

证明了Location Independent Riskier Order随机序关系关于简单随机样本的极小值与可微递增凹变换的封闭性质，并讨论了Dilation序关系的一些矩不等式．     

随机时间剩余寿命的分布类性质

得出了随机时间剩余寿命XY的随机比较性质和矩不等式．当Y是指数分布时求出了XY的故障率的界．     

Right Spread序的若干封闭性质

§1Introductionandmotivation Itisalwaysofinteresttocomparethevariabilityoftworandomvariablesinreliability theoryandeconomics.Thecomparisonsbasedonmomentssuchasvarianceandstandard deviationarenotveryinformativealthoughsuchmeasuresaresimpletouse.Meanwhile,sincethesecomparisonsarestaticones,andhencetheirapplicationsinsomefields,e.g.,reliabilityandfinance,arerestricted.Inthesefields,however,somedynamicalcomparisons areneeded.Asaresult,severalstochasticordersthataremorerefinedhavebeen establishedi…     

序半群的若干等价性质

本主要建立了序半群S中N-类的单性与S的关于其元素和理想的某些性质之间的等介关系。     

关于Domain范畴的若干性质

给出保逼近序的Scott连续伴随的等价刻划,在此基础上建立了几类以保逼近序的Scott连续函数为态射的Dom ain 范畴,并得到了这些范畴的一系列性质     

集值序增过程及其性质

首先给出有界闭凸集值序增函数以及有界闭凸集序增过程的定义;然后讨论了有界闭凸集值序增函数以及有界闭凸集值序增过程的性质.     

����DMRL������ɽ���

Let and be two nonnegative absolutely continuous random variables with respective distribution functions and such that, right-continuous inverse functions and, and survival functions and, respectively. We write, and say is smaller than in the DMRL (decreasing mean residual life) order, if the function is increasing in. Some characterization properties of the DMRL order are investigated. The closure and reversed closure properties of the DMRL order are obtained. Meanwhile, some illustrative examples that meet the DMRL order are shown as well.     

Two suggestions of how to define a stochastic stress-strength system

In this paper we suggest how to generalize a stress-strength system treated in Ebrahimi (1984) at a fixed point of time to a dynamic situation in two ways. In the first approach we assume that a stress factor starts and stops to influence the system and different stress factors add up to total system stress at any time. In the second approach we assume that a stress factors starts and stops to influence the system and stress factors do not accumulate additively.     

Proximity between life distributions and exponential distributions (I)

Many classes of life distributions have been introduced into reliability theory. Because of the importance of exponential distributions in reliability theory, it is interesting to study the difference between life distributions and exponential distributions. In this paper, we study the proximity between the life distribution in various classes and the exponential distribution. We shall give some simple upper bounds.This research was partially supported by the National Natural Science Foundation of China.     

SOME NEW PARTIAL ORDERINGSDESCRIBING AGING PROPERTY

The concept of aging, which is very users in relability describes the adverse orbeneficial effects of age on the lifetime of systems. Several partial orderings of life distributionshave been introduced. In this article,some more partial orderings of life distributions are imtroduced mainly by means of the equilibrium distribution. And conversely, a group of new aging clasps oflife distrbutions can be derived from these orderings.     

Majorization and arrangement orderings in open queueing networks

Consider an open Jackson network of queues. Majorization and arrangement orderings are studied to order, respectively, various loading and server-assignment policies. It is shown that under these order relations, stochastic and likelihood ratio orderings can be established for the maximum and the minimum queue lengths and for the total number of jobs in the network. Stochastic majorization and stochastic orderings are also established, respectively, for the queue-length vector and the associated order-statistic vector. Implications of the results on loading and assignment decisions are discussed.     

New multivariate orderings based on conditional distributions

In this paper, we propose and study new multivariate extensions of the dispersive, right‐spread, decreasing mean residual life and new better than used in expectation univariate orders. These new orders are based on the comparison of univariate marginal distributions conditional on survival data for the rest of the components. Relationships among multivariate orders and applications to some multivariate random vectors are also provided. Copyright © 2011 John Wiley & Sons, Ltd.     

Inheriting independence and chi-squaredness under certain matrix orderings

Let x ～ N(μ, Z), and let S = (Σ:μ). It is shown that if x′A₁x is independent of x′Bx (x′A₁x is distributed as a chi-square variable), then this property is inherited by every x′A₂x for which S′A₂S precedes S′A₁S with respect to the range preordering (with respect to the rank subtractivity partial ordering).     

Some partial orderings of exchangeable random variables by positive dependence

Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such partial orderings are then discussed. Particular examples include ordering multivariate normal, t, χ², Cauchy, exponential, binomial, Poisson, gamma and Farlie-Gumbel-Morgenstern random vectors. Applications to genetic selection and choice of sampling procedures are given.