基于分散型和扩散型随机序对几种寿命分布类的刻画

本文基于分散型和(或)扩散型随机序，利用随机变量的剩余寿命给出了寿命分布类ILR，IFR，DMRL和IFR(2)及其对偶类的刻画．作为主要结果的一个应用，用k／n-系统的剩余寿命对IFR和DMRLS及其对偶类进行了刻画．这些结果拓宽和加强了文献中已有的结果．     

关于随机序的一个注记

本文引入随机序(≤_d)的概念,说明在讨论随机变量列的依概率(依分布)收敛问题时,它是一个颇为恰当的“控制尺度”.     

逆Weibull分布随机变量的随机比较

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

Ⅰ型极值分布随机变量的随机比较

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

记录值中的随机序与年龄性质

研究记录值中的随机序与年龄性质．证明了任何通过两个分布函数的行为所定义的随机序,均可以被它们相应的记录值所保持,而两个随机变量之间的剩余财富序,可以导致其相应记录值序列的平均连续增量的序关系．也讨论了K-记录值的连续增量的年龄性质．     

逆Weibull分布随机变量的随机比较(英文)

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Ⅰ型极值分布随机变量的随机比较(英文)

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

任意随机变量序列关于随机选择的一类强偏差定理

本文通过引进极限相对对数似然比,利用限制似然比给出了样本空间的一个子集,得到了任意实值随机变量序列关于随机选择的一类用不等式表示的强极限定理.并作为推论得到了任意整值随机变量序列的m元序组的强偏差定理.     

关于Tsallis熵与随机序的一些结果

本文讨论了具有相同Tsallis熵或相同Tsallis相对熵的两个连续随机变量随机等价的一些条件,以及随机序与Tsallis熵序的一些关系.     

随机寿命间的TTT序关系的一个非参数检验

本文先建立了一个具有TTT序关系的两个非负随机变量之间距离的概率度量，然后构造了一个非参数检验方法以判断严格的TTT序关系，利用L-统计理论获得了检验统计量的渐近分布，数值模拟的结果也表明该方法的性能是令人满意的．     

Second Order Stochastic Inclusion

Abstract

The purpose of the paper is to consider some stochastic control problems as a particular case of a more general theory, the stochastic inclusions theory. We discuss the existence of weak solutions to a stochastic inclusion of second order, driven by two general semimartingales. Finally we present some examples.     

关于随机阶的几个结果

在较弱条件下,对独立随机变量序列的极大值序列,给出了几个关于随机阶的结果.     

Nonparametric Bayesian Modeling for Stochastic Order

In comparing two populations, sometimes a model incorporating stochastic order is desired. Customarily, such modeling is done parametrically. The objective of this paper is to formulate nonparametric (possibly semiparametric) stochastic order specifications providing richer, more flexible modeling. We adopt a fully Bayesian approach using Dirichlet process mixing. An attractive feature of the Bayesian approach is that full inference is available regarding the population distributions. Prior information can conveniently be incorporated. Also, prior stochastic order is preserved to the posterior analysis. Apart from the two sample setting, the approach handles the matched pairs problem, the k-sample slippage problem, ordered ANOVA and ordered regression models. We illustrate by comparing two rather small samples, one of diabetic men, the other of diabetic women. Measurements are of androstenedione levels. Males are anticipated to produce levels which will tend to be higher than those of females.     

Sequential Order Statistics: Ageing and Stochastic Orderings

Ordered random variables play an important role in statistics, reliability theory, and many applied areas. Sequential order statistics provide a unified approach to a variety of models of ordered random variables. We investigate conditions on the underlying distribution functions on which the sequential order statistics are based, to obtain stochastic comparisons of sequential order statistics given some well known stochastic orderings, such as the usual stochastic, the hazard rate and the likelihood ratio orders, among others. Also, we derive sufficient conditions under which the sequential order statistics are increasing hazard rate, increasing hazard rate average or decreasing hazard rate average. Applications of the main results involving nonhomogeneous pure birth processes are also given.     

Preference Order Stochastic Knapsack Problems: Methodological Issues

A preference order dynamic programming model proposed in the literature for solving stochastic knapsack problems is shown to be somewhat limited from both the methodological and computational points of view. A counterexample is presented contradicting the optimality of a procedure designed for normal variates.     

关于Gamma分布的秩序统计量的随机比较

对于独立不同分布的两个Gamma样本，当它们相同的形状参数大于或等于1时，最近Korwar(2002)证明了，当它们的尺度参数满足优化序时，样本的卷积就满足似然比序．本文我们证明了，当Gamma分布的形状参数小于1时，样本的对应秩序统计量之间存在一致的一般随机序；然而当形状参数大于1时，样本对应的极大值和极小值统计量有着相反的一般随机序。     

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.     

Stochastic Comparisons and Dependence among Concomitants of Order Statistics

Let (X_i, Y_i) i=1, 2, …, n be n independent and identically distributed random variables from some continuous bivariate distribution. If X_(r) denotes the rth ordered X-variate then the Y-variate, Y_[r], paired with X_(r) is called the concomitant of the rth order statistic. In this paper we obtain new general results on stochastic comparisons and dependence among concomitants of order statistics under different types of dependence between the parent random variables X and Y. The results obtained apply to any distribution with monotone dependence between X and Y. In particular, when X and Y are likelihood ratio dependent, it is shown that the successive concomitants of order statistics are increasing according to likelihood ratio ordering and they are TP₂ dependent in pairs. If we assume that the conditional hazard rate of Y given X=x is decreasing in x, then the concomitants are increasing according to hazard rate ordering and are dependent according to the right corner set increasing property. Finally, it is proved that if Y is stochastically increasing in X, then the concomitants of order statistics are stochastically increasing and are associated. Analogous results are obtained when the variables X and Y are negatively dependent. We also prove that if the hazard rate of the conditional distribution of Y given X=x is decreasing in x and y, then the concomitants have DFR (decreasing failure rate) distributions and are ordered according to dispersive ordering.     

Boundary Value Problems for First Order Stochastic Differential Equations

In this paper, we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition （in the sense of expectation）. Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value. Then by using the contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the existence theorem. Finally, we explain our main results by an elementary example.     

广义次序统计量间隔的多维随机排序

本文研究了附加于广义次序统计量底分布以及参数的条件, 使得人们在多维似然比序和多维通常随机序意义下对广义次序统计量的间隔向量进行比较, 同时也给出了文中主要结果的应用.