位置参数估计量的损失函数之估计

本文考虑损失函数的估计问题,分别对于球对称分布和均匀分布情形给出了其参数的J-S型估计量的损失之估计,它们满足[1]中提出的条件(Ⅰ)和(Ⅱ).     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

多元Liouville分布的进一步探讨及一些有关分布

本文继[1]、[2]两文之后进一步讨论了多元Liouville分布(ML分布)的一些性质,去掉了[1]、[2]两文中关于独立性刻划的附加限制,同时论证了部分多个分量之和在ML分布中的重要地位,并由此得出了ML分布的边缘刻划。另外也给出了刻度不变统计量关于ML分布类的一些良好性质,并将上述结果应用于广义多元Liouville分布(GML分布)及其它有关分布类的讨论。     

RiskMetrics模型评估与扩展

RiskMetrics是当今最为流行的风险度量模型,然而其基础假设-标准化收益服从正态分布,却备受置疑.放宽此假设,以更灵活的t分布,广义误差分布,混合正态分布,Johnson Su-正态,Pearson IV分布代替,建立了五种扩展的RiskMetrics模型.我们用沪深股市日收益数据进行实证比较分析,回测结果表明,扩展模型明显优于标准模型,而基于非对称分布假设的模型优于基于对称分布的模型.     

带分布时滞的高阶微分不等式及其应用

本文研究了带有分布时滞的高阶中立型微分不等式最终正解的问题.运用反证法,我们得到了带有分布时滞的高阶中立型微分不等式不存在最终正解的若干新的准则.所得定理推广和改进了文献中的结果.     

自适应逐步Ⅱ型混合删失下威布尔分布的参数估计

在可靠性试验中,自适应逐步Ⅱ型删失机制是Ⅰ型删失和逐步Ⅱ型删失机制的混合。Weibull分布一直是可靠性寿命试验的常用分布函数。在自适应逐步Ⅱ型删失机制下,给出分布中参数的极大似然估计,同时在样本量较小时给出boostrap纠正偏差估计量,并用数值模拟的方法验证估计结果的效果。     

从偏态Pearson Ⅶ分布生成的新的多元偏态t分布

一般而言,偏态的椭球等高分布是一类分布族,有相当一部分的分布都是积分形式,且此类积分不易求出,而偏态的正态、偏态的正态尺度混合、偏态的PⅦ型、偏态的PⅡ型的分布却有着很好的结构,偏态t分布属于偏态PⅦ型分布,因此,本文在偏态PⅦ型分布的基础上着重研究新的偏态t分布,给出它的背景、定义、两种随机表示及其等价性.     

逐步增加Ⅱ型截尾下Pareto分布的Bayes估计

基于逐步增加的Ⅱ型截尾样本,当Pareto分布的尺度参数已知时,分别在平方损失和LINEX损失下讨论了其形状参数和可靠性指标(失效率和可靠度)的Bayes估计,并用Monte-Carlo方法对估计结果的MSE,进行了模拟比较.结果表明了在LINEX损失下的估计结果更有效.     

基于混合Ⅰ型删失数据的威布尔模型精确推断（英文）

威布尔分布是可靠性和寿命测试试验中常用的模型.本文中,我们考虑了基于混合Ⅰ型删失数据的威布尔模型精确推断.我们得到了威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,我们也给出了未知参数的另外几种置信区间,比如,基于近似方法的置信区间,Bootstrap置信区间.为了评价本文的方法,我们给出了一些数值模拟的结果.     

基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划(英文)

本文考虑基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划.得到威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,给出未知参数的另外几种置信区间,基于近似方法的置信区间.为了评价本文的方法,给出一些数值模拟的结果.且讨论了可靠性中的可接受抽样计划问题.利用参数最大似然估计的精确分布,给出一个可接受抽样计划的执行程序和数值模拟结果.     

Skew Models II

If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.      

A family of kurtosis orderings for multivariate distributions

In this paper, a family of kurtosis orderings for multivariate distributions is proposed and studied. Each ordering characterizes in an affine invariant sense the movement of probability mass from the “shoulders” of a distribution to either the center or the tails or both. All even moments of the Mahalanobis distance of a random vector from its mean (if exists) preserve a subfamily of the orderings. For elliptically symmetric distributions, each ordering determines the distributions up to affine equivalence. As applications, the orderings are used to study elliptically symmetric distributions. Ordering results are established for three important families of elliptically symmetric distributions: Kotz type distributions, Pearson Type VII distributions, and Pearson Type II distributions.     

多元正态分布的VDR条件拟合优度检验

提出多元正态性χ2检验统计量.多元正态分布转换样本Yd=RVd服从PearsonII型分布,证明了R2服从贝塔分布.基于贝塔分布和单位球均匀分布,得到多元正态性检验统计量χ2的渐近卡方分布.功效模拟显示,χ2统计量优于已有主要多元正态性检验统计量.做iris数据多元正态性的拟合优度检验.     

Noncentral elliptical configuration density

The noncentral configuration density, derived under an elliptical model, generalizes and corrects the Gaussian configuration and some Pearson results. Partition theory is then used to obtain explicit configuration densities associated with matrix variate symmetric Kotz type distributions (including the normal distribution), matrix variate Pearson type VII distributions (including t and Cauchy distributions), the matrix variate symmetric Bessel distribution (including the Laplace distribution) and the matrix variate symmetric Jensen-logistic distribution.     

On Mardia's and Song's measures of kurtosis in elliptical distributions

The main objective of this paper is the calculation and the comparative study of two general measures of multivariate kurtosis, namely Mardia's measure β_2,p and Song's measure S(f). In this context, general formulas for the said measures are derived for the broad family of the elliptically contoured symmetric distributions and also for specific members of this family, like the multivariate t-distribution, the multivariate Pearson type II, the multivariate Pearson type VII, the multivariate symmetric Kotz type distribution and the uniform distribution in the unit sphere. Analytic expressions for computing Shannon and Rényi entropies are obtained under the elliptic family. The behaviour of Mardia's and Song's measures, their similarities and differences, possible interpretations and uses in practice are investigated by comparing them in specific members of the elliptic family of multivariate distributions. An empirical estimator of Song's measure is moreover proposed and its asymptotic distribution is investigated under the elliptic family of multivariate distributions.     

Distributions Minimizing Fisher Information for Location in Kolmogorov Neighbourhoods

This paper is concerned with the problem of finding those distributionsminimizing Fisher information for location over Kolmogorov neighbourhoods ofdistribution functions G satisfying certain mild conditions. The case when Gis symmetric has been considered by quite a few authors. The general form ofthe solution is discussed. Furthermore we provide the solution of twoasymmetric distributions, namely, the extreme value distribution and thePearson's type IV distribution.     

Singular random matrix decompositions: distributions

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and pseudo-Wishart generalized singular and non-singular distributions. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.     

从偏态Pearson VII分布生成的新的多元偏态t分布

一般而言, 偏态的椭球等高分布是一类分布族,有相当一部分的分布都是积分形式, 且此类积分不易求出,而偏态的正态、偏态的正态尺度混合、偏态的PVII型、偏态的PII型的分布却有着很好的结构,偏态t分布属于偏态PVII型分布, 因此,本文在偏态PVII型分布的基础上着重研究新的偏态t分布,给出它的背景、定义、两种随机表示及其等价性.