学生成绩的相关分析

本文提供了在多维随机变量中寻找主成分的一种方法 ,证明了其余分量均可表示为主成分的线性组合 ,解决了多维随机变量的各个分量之间所存在的线性关系问题 .通过用本文的方法对两个学期的 14门课的学生成绩进行相关分析并找出了主成分及与之相关的课程 ,比较了与相关系数矩阵的不同 ,也讨论了课程设置的合理性     

多维指数分布模型

运用 Marshall-Olkin推导二维指数分布的思路 ,提出七个相互独立冲击源的冲击模型 ,构造了三维指数分布 .鉴于该方法分析过程繁琐 ,难于推广到高维情形 .文中另辟溪径 ,利用作者已建立的多维失效率与分布密度函数间的关系 ,并结合致命冲击的含义 ,得到三维乃至一般的 n维指数分布 .     

关于局部次指数分布的一个注记

通过次指数密度函数建立了局部次指数分布类的一个等价刻画.作为其应用,我们证明了局部次指数分布类不具有卷积封闭性.     

二元Freund型指数分布的独立性和不相关性

本文讨论二元Freund型指数分布的独立性和不相关性,分别获得了两个服从二元Freund型指数分布随机变量相互独立及不相关的充分必要条件;并得到了其相关系数的精确表达式,证明了在对称情形其相关系数落入负三分之一与一之间,文末证明了X,Y之间的渐近独立性.     

二元Arnold-Strauss型指数分布的条件指数性及渐近独立性

本文讨论二元Arnold-Strauss型指数分布的条件指数性及渐近独立性,证明了给定X关于Y的条件密度和给定Y关于X的条件密度都是指数分布密度,求出了用于预报的条件概率;并证明了X,Y之间的渐近独立性.另外,讨论了它的识别性,若已知可识最小值的分布密度时,所有参数皆可识别.     

一种基于多维尾条件期望的扩散模型检验方法

为了解决多维扩散模型的设定检验问题,我们基于多维尾条件期望(CTE)制定了一个检验统计量.虽然不能直接估计出多维扩散模型的转移密度矩阵,但是可以估计出每个分量的转移密度,再通过CTE将每个分量联合起来,建立了一个真正的多维统计量.最后通过仿真模拟评估了该检验方法的检验的性能.     

多维对称随机变量分布函数的充要条件

讨论了多维对称随机变量的若干性质,阐明其分量仍是对称随机变量,在此基础上,进一步给出多维对称随机变量分布函数的一个充分必要条件.     

基于多维角色的访问控制模型

针对RBAC应用系统中角色具有多层语义的特点,提出了多维角色访问控制模型.模型中角色用多维角色分量表示,给出了在角色分量上定义角色层次、角色限制和角色权限指派关系的方法,使角色的语义清晰,简化了模型的角色管理和角色的权限分配.     

双参数指数截尾分布参数估计相合性的证明

给出了双参数指数分布截尾寿命试验样本的联合分布,得到了参数的极大似然估计,并证明了该估计的相合性.     

一类新的二参数二元混合型指数分布的参数估计及相关结构

本文继续文[13]的工作,针对二元Marshall-Olkin型指数分布随机结构模型,取掉一个服从指数分布的随机变量,从而导出一类二参数二元混合型指数分布,并由此研究了它的特征和参数估计及相关结构;通过密度分拆重组技术,本文导出了一类二参数二元混合型指数分布的一个特征,据此,获得了基于总体(X,Y)完全样本的参数的最大似然估计及一致最小方差无偏估计,计算了两个随机变量之间的相关系数,证明了其相关系数的取值落在(0,1)区间内.     

STRUCTURES OF SYSTEMS WITH EXPONENTIAL LIFE DISTRIBUTIONS

Abstract. Structures of monotone systems and cold standby systems with     

Convolutions of multivariate phase-type distributions

This paper is concerned with multivariate phase-type distributions introduced by Assaf et al. (1984). We show that the sum of two independent bivariate vectors each with a bivariate phase-type distribution is again bivariate phase-type and that this is no longer true for higher dimensions. Further, we show that the distribution of the sum over different components of a vector with multivariate phase-type distribution is not necessarily multivariate phase-type either, if the dimension of the components is two or larger.     

Some properties and an application of multivariate exponential polynomials

In the paper, the authors introduce a notion “multivariate exponential polynomials” which generalize exponential numbers and polynomials, establish explicit formulas, inversion formulas, and recurrence relations for multivariate exponential polynomials in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, two identities for the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, construct some determinantal inequalities and product inequalities for multivariate exponential polynomials with the aid of some properties of completely monotonic functions and other known results, derive the logarithmic convexity and logarithmic concavity for multivariate exponential polynomials, and finally find an application of multivariate exponential polynomials to white noise distribution theory by confirming that multivariate exponential polynomials satisfy conditions for sequences required in white noise distribution theory.     

Sequential order statistics with an order statistics prior

In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated.     

Multivariate dynamic information

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.     

Reliability of multi-component stress–strength models

In this paper, we estimate the reliability of some parallel and series multi-component stress–strength models. We determine the reliability of a system composed of k dependent components subjected to n dependent stresses. We study the cases, when the components are either arranged in series or in parallel. The components strengths are assumed to have (k + 1)-parameter multivariate Marshall–Olkin exponential distribution, while the stresses are (n + 1)-parameter multivariate Marshall–Olkin exponentially distributed.     

On the DFR property of the compound geometric distribution with applications in risk theory

In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution.     

On the DFR property of the compound geometric distribution with applications in risk theory

In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution.     

Unbiased Estimation for a Multivariate Exponential whose Components have a Common Shift

It is shown that for independent and identically distributed random vectors, for which the components are independent and exponentially distributed with a common shift, we can construct unbiased estimators of their density, derived from the Uniform Minimum Variance Unbiased Estimator (UMVUE) of their distribution function. As direct applications of the UMVUEs of the density functions we present a Chi-square goodness of fit test of the model, and give two tables of the UMVUEs of some commonly used functions of the unknown parameters of the multivariate exponential model considered in this paper.