线性模型中不可估参数的线性估计的可容许性

对一般线性模型在平方损失函数下，得到了一维不可估参数函数的线性估计为可容许估计的充要条件，以及模型中参数向量（非线性可估）的线性估计为可容许估计的两个充要条件，并得到了多维参数函数（可估或不可估）的线性估计为可容许估计的一个充分条件以及特殊情况下的一个充要条件．     

多元线性模型中随机回归系数和参数的线性估计的泛容许性

本文对于一般的随机效应多元线性模型，给出了随机回归系数和参数的线性可估函数的泛容许性估计的定义，并得到了随机回归系数和参数的线性可估函数的齐线性估计在齐线性估计类中泛容许性的特征。     

多元线性模型中共同均值参数的线性估计的可容许性

本文讨论了多元线性模型中共同均值参数的估计问题，针对矩阵损失函数，给出了五种不同形式的优良性准则，证明了在齐次和非齐次性估计中分别是一致的，并且得到了在相应的估计类中均值参数矩阵的线性可估函数的线性估计的可容许性特征。     

离散参数空间平方损失下的可容许估计

50年代以来,许多统计工作者对单参数指数分布族中参数的可容许性(平方损失下)作了较多讨论,给出了一些线性和非线性(主要的是有理函数)的可容许估计.这些内容可参看文献[1—8].文献[9—11]分别在前面的基础上给出了在平方损失下关于 L 测度几乎可容许估计的一般性定理.这些文献所讨论的参数空间是实数空间上有限或无限的连续区间.本文将讨论离散参数空间(?)={θ_k:θ_k∈R~1,k=1,2,…}.第二节对离散参数空间在平方损失函数 L(g(θ),d)=λ(θ)(d-g(θ))~2下,给出参数函数 g(θ)的估计是可容许的充分条件,第三节以二项分布与爱尔兰分布为例说明了该定理的应用.     

熵损失函数下两参数Lomax分布形状参数的Bayes估计

在熵损失函数下,讨论了两参数Lomax分布形状参数的Bayes估计和可容许估计.并讨论了一类(cT+d)~(-1)形式估计的可容许性和不可容许性.     

具有特殊协方差结构的 SURE 模型中参数估计的若干结果

本文讨论具有特殊协方差结构似乎不相关回归方程（SURE）模型中参数的估计问题．除非另有说明,损失函数将取为二次损失和矩阵损失．本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的;还分别在仿射交换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变（UMRE）估计的充要条件,并证明了在仿射交换和二次损失下不存在协方差阵和方差的UMRE估计．     

一种对称损失函数下正态总体刻度参数的估计

本文研究正态分布中刻度参数在损失函数L(σ，δ)=[(σ-δ)^2]/σδ下的最小风险同变估计及Bayes估计，并讨论(cT(x) d)^1/2形式估计的可容许性与不可容许性，我们发现在这种损失下σ的极大似然估计是不可容许的．     

连续型多参数指数族参数的渐近最优的经验Bayes估计

§1 引言关于单参数经验 Bayes(EB)估计问题,目前讨论已经比较多了,但多参数的 EB 估计问题讨论的较少.最近陶波在[1]中讨论了正态分布 N(μ,σ~2)之参数θ=(μ,σ~2)的两参数 EB估计的渐近最优(a.o.)性.关于指数族的 a.o.EB 估计问题,陈希孺在[2]中讨论了一维离散型单参数指数族参数的 EB 估计的 a.o.性.本文考虑连续型多参数指数族参数的 EB 估     

矩阵损失下多维 POISSON 均值的线性估计的可容许性

设 X_1…,X_n 相互独立,X_i 遵从参数为λ_i 的 Poisson 分布.L.D.Brown 和 R.H.Farrell 在[1]中阐述了λ=(λ_1,…,λ_n)′的线性估计的实际意义,并在二次损失函数下给出了λ的线性估计是可容许的充要条件.本文在[2]和[3]等使用的矩阵损失函数(d-λ)(d-λ)′下讨论λ的线性估计,在线性估计类中的可容许性.注意到λ的线性估计的风险函数只涉及 X=(X_1,…,X_n)′     

带约束一般生长曲线模型中可容许线性估计的特征

本文讨论带约束一般生长曲线模型中的可容许线性估计问题,对于回归系数的线性可估函数KBL的估计DYF(DYF+M),分别在齐次和非齐次线性估计类中,给出了它们是可容许估计的一些特征.     

A note on the moments of order statistics from doubly truncated exponential distribution

Summary In a recent paper [2], the author has obtained some recurrence relations between the moments of order statitics from the exponential and right truncated exponential distributions. In this paper, similar relations are derived for a doubly truncated exponential distribution. It is shown that one can obtain all the moments by using these recurrence relations.     

k-正态分布及其应用

近本文研究了截断随机变量和k-正态分布.利用对数凹函数理论,获得了涉及截断随机变量和截断随机变量的函数的方差的不等式链,推广了涉及正态分布和分层教学模型的一些经典结论.同时在附录部分给出了仿真结果.     

A truncated Cauchy distribution

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.     

Study of cut-set distributions in the fuzzy reliability evaluation models

The performances of the cut-set distributions in the fuzzy reliability evaluation are studied based on cut-set method. Firstly, a theorem is proved to indicate the convergence defect of the model with the three commonly used cut-set distributions, including uniform distribution, linear distribution and truncated normal distribution. Secondly, a general method is proposed to construct a new family of cut-set distributions named intrinsic cut-set distributions, and three specific intrinsic cut-set distributions are obtained based on this method, including modified truncated normal distribution, truncated lognormal distribution and truncated Weibull distribution. Thirdly, numerical examples are carried out to verify the above theoretical results. It is shown that, compared with the three commonly used cut-set distributions, the proposed intrinsic cut-set distributions make the evaluation more stable and the fuzzy reliability model achieve good convergence at the boundary cases, which could effectively improve the evaluation accuracy and broaden the application of the model. Finally, some recommendations are given to show how to choose a suitable cut-set distribution in practice.     

Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring

This paper deals with the optimal designing of step-stress partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions under censoring. It is assumed that the lifetime of the items follow truncated logistic distribution truncated at point zero. Truncated distributions arise when sample selection is not possible in some sub-region of the sample space. The logistic distribution is considered inappropriate for modeling lifetime data because left hand side of its distribution extends to negative infinity, and this could conceivably result in modeling negative times-to-failure. This has necessitated the use of truncated logistic distribution truncated at point zero for modeling lifetime data. Unlike the widely studied exponential, Weibull and lognormal life distributions, the failure rate of truncated logistic distribution is increasing and more realistically bounded below and above by non-zero finite quantity. The optimal change-time for the step PALT is determined by minimizing either the generalized asymptotic variance of maximum likelihood estimates (MLEs) of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor. Inferential procedure involving model parameters and acceleration factor are studied. Sensitivity analysis is also performed.     

A model for the corona of a spherical star cluster

A general model for the outer layers of steady spherical star systems is considered. The corona is assumed to be formed by stars flying out of the system along ballistic orbits. Expressions for density runs and velocity dispersions are found. Models of three kinds are studied, namely, systems with isotropic velocity distribution, spheres with purely radial orbits, and models with ellipsoidal velocity distribution. The following isotropic distribution functions were considered as examples: the truncated Maxwellian distribution, King’s model, and the spherical analogue of Perek’s model. The truncated Maxwellian distribution of radial velocities is an example of a radial orbit system. The truncated Schwarzschildian velocity distribution and generalized polytropes introduced by Kuzmin and Veltmann are examples of models with ellipsoidal velocity distribution. Density asymptotics are found for all models provided that the self-gravitation of coronas is neglected.     

双边截断分布族中的卷积定理与渐近有效性

在具有共同支撑的分布族与单边截断分布族中,Ｂｉｃｋｌｅ Ｐ．Ｊ, Ｉｂｒａｇｉｍｏｖ　Ｉ． Ａ． 与 Ｈａｓｍｉｎｓｋｉｉ Ｒ． Ｚ．证明了两个重要的卷积定理．在本文中,我们考虑如下的双边截断分布族：ｄＰθ（ｘ）＝ ｆ（ｘ; θ１, θ２）Ｉ（θ１≤ｘ≤ θ２）ｄｘ,其中θ＝（θ１, θ２）, θ１＜ θ２为未知 待估参数．在较弱的条件下,我们得到了关于此分布族的卷积定理．并且,基于此卷 积定理的结论,提出了一个参数函数渐近有效性的定义．在本文结束之时,对于一个 双边截断分布族,给出了具有此渐近有效性的参数函数的估计．     

基于涨跌幅限制的双边截断正态分布期权定价模型

标准Black Scholes期权定价公式假设股票价格服从对数正态分布,没有考虑股票价格涨跌幅的限制带来的影响.放松该假设条件,假设股票价格服从双边截断对数正态分布,考虑中国股票市场的涨跌幅限制,得到一个新的B-S期权定价公式来表达股价行为.双边截断正态分布假设下收益率的波动率要要比正态分布下的波动率小,所以新B-S公式计算出的期权价格就会比标准B-S公式计算出的价格低.     

Em algorithm of the truncated multinormal distribution with linear restriction on the variables

A new expectation-maximization (EM) algorithm is proposed to estimate the parameters of the truncated multinormal distribution with linear restriction on the variables. Compared with the generalized method of moments (GMM) estimation and the maximum likelihood estimation (MLE) for the truncated multivariate normal distribution, the EM algorithm features in fast calculation and high accuracy which are shown in the simulation results. For the real data of the national college entrance exams (NCEE), we estimate the distribution of the NCEE examinees’ scores in Anhui, 2003, who were admitted to the university of science and technology of China (USTC). Based on our analysis, we have also given the ratio truncated by the NCEE admission line of USTC in Anhui, 2003.     

Some General Characterizations of the Bivariate Gumbel Distribution and the Bivariate Lomax Distribution Based on Truncated Expectations

Recently attempts have been made to characterize probability distributions via truncated expectations in both univariate and multivariate cases. In this paper we will use a well known theorem of Lau and Rao (1982) to obtain some characterization results, based on the truncated expectations of a functionh, for the bivariate Gumbel distribution, a bivariate Lomax distribution, and a bivariate power distribution. The results of the paper subsume some earlier results appearing in the literature.