二参数广义Rayleigh分布

为了研究某些工程过程的寿命,需要一个能够适应这些过程性质的寿命模型.与简单模型相比,基于寿命分布的广义模型在建模过程中更具有直观的适用性和吸引力.本文介绍一个二参数广义Rayleigh分布,推导出了其矩生成函数和k阶矩的表达式,通过对样本点进行归一化,得到了它的近似分布函数、概率密度函数、生存函数、风险率函数等.在此基...     

F分布密度函数之性质

本文利用特殊函数的性质,较详细地分析了F分布密度函数之性质,指出了该密度函数与相应参数之间的关系.本文主要研究第二个参数变化对密度函数的影响,证明了n增大时F(m,n)分布的密度函数极大值也越来越大,还指出了n变化时F(m,n)分布的相应密度曲线与另一特定密度曲线交点的变化规律.     

斜t及斜Laplace分布

本文首先介绍一种用来处理重尾数据的斜t分布,并给出其相应的基本数字特征.基于Laplace分布的对称性及重尾性,定义一种新的分布一斜Laplace分布,推导出新分布的密度函数和分布函数,且通过密度函数曲线图书其与Laplace分布进行比较.最后,证实所提斜Laplace分布的重尾性质.     

M函数的极限性质

M函数是一类特殊的级数,常用于计算冲击模型的寿命分布,本文主要讨论了M函数在其参数δ及参数x趋向无穷大和趋向零的情形下的极限,从而得到了M函数的三个极限性质,进而,利用M函数的极限性质给出了滤过泊松过程一阶矩的简洁证明.     

同分布ρ-混合序列的最大值不等式及其应用

本文讨论了同分布混合序列部分和分布函数的上界及其应用.利用矩不等式和截尾方法,得到了部分和分布函数的上界.作为应用,并且极大值函数的矩存在的充分条件,与独立时的结果是一致的.     

记录时及相应计数过程关于矩精确完全收敛的渐进性质（英文）

我们考虑一列独立同分布且分布函数绝对连续的随机变量序列及其记录时和相应的计数过程,得到了记录时和相应计数过程的关于矩精确完全收敛的渐进性质.     

�����ڷ����Ǹ����ݵ�ָ����������̬�ֲ�

本文研究了一种可用于分析非负数据的新的分布族. 它用一个随机表示来定义, 是一个半正态随机变量与一个指数随机变量的幂的混合. 其密度函数和性质, 包括风险函数, 矩和矩母函数被导出. 该分布族的实用性和灵活性通过一个实例用最大似然程序被阐明.     

参数的变化对F分布密度函数之影响

该文运用对无穷级数的一些特殊处理方法,深入分析了与Γ函数有关的一些特殊函数的性质,揭示了参数变化时F分布密度函数极值变化的一些深刻规律.该文指明,n增大时F分布的密度函数f_{m,n}(x)的极大值单调增加,而m增大时该密度函数的极大值或单调减少,或先减后增.     

Copula函数中参数的矩估计方法

Copula函数是将多维随机变量的联合分布和其边缘分布连接起来的一种函数.关于Copula函数的理论和应用已有不同深度的研究,特别是Copula函数中未知参数的估计问题.本文研究了Gumbel Copula函数的参数估计,提出了矩估计和近似矩估计两种方法,分别得到了未知参数的估计结果,并通过模拟研究对这两种方法进行了比较,结果显示矩估计方法更为合理.     

T-IPH分布的若干性质及其在排队论中的应用

本文讨论T-IPH分布的一些重要性质,其中T-IPH表示可数状态离散时间吸收生灭链吸收时间的分布.对该分布,首先给出了其概率生成函数(PGF),在此基础上,进~步给出了计算分布概率分布律以及阶乘矩数值结果的迭代公式.另外,还讨论了T-IPH分布在排队论中的一个应用.     

绕积马氏链的中心极限定理

讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件.     

The skew elliptical distributions and their quadratic forms

In this paper, a family of the skew elliptical distributions is defined and investigated. Some basic properties, such as stochastic representation, marginal and conditional distributions, distribution under linear transformations, moments and moment generating function are derived. The joint distribution of several quadratic forms is obtained. An example is given to show that the distributions of some statistics as the functions of the quadratic forms can be derived for various applications.     

A Skew Laplace Distribution on Integers

We propose a discrete version of the skew Laplace distribution. In contrast with the discrete normal distribution, here closed form expressions are available for the probability density function, the distribution function, the characteristic function, the mean, and the variance. We show that this distribution on integers shares many properties of the skew Laplace distribution on the real line, including unimodality, infinite divisibility, closure properties with respect to geometric compounding, and a maximum entropy property. We also discuss statistical issues of estimation under this model.     

Inferences in linear mixed models with skew-normal random effects

For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran's theorem is given, which modifies the result of Wang et al. (2009) and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.     

Testing skew normality via the moment generating function

In this paper, goodness-of-fit tests are constructed for the skew normal law. The proposed tests utilize the fact that the moment generating function of the skew normal variable satisfies a simple differential equation. The empirical counterpart of this equation, involving the empiricalmoment generating function, yields appropriate test statistics. The consistency of the tests is investigated under general assumptions, and the finite-sample behavior of the proposed method is investigated via a parametric bootstrap procedure.     

一般随机环境中马氏链的强大数律

本文研究了具有离散参数的一般环境中马氏链的强大数定律.利用随机环境中马氏链停时,获得了加在绕积马氏链样本函数上大数定律成立的充分条件.     

A new construction for skew multivariate distributions

This paper considers a new approach to develop a very general class of skew multivariate distributions. The approach is based on a linear combination of an elliptically distributed random variable with a linear constraint. Using this approach two different classes of multivariate distributions are constructed based on original distribution. These new classes include different types of skew normal (type A and type B) and other skew elliptical distributions, exist in the literature. We also derive the moment generating function, marginal and conditional density of our proposed classes of distributions. Straightforward explanations are applied to demonstrate the relationships among previous approaches by others with our proposed class of skew distributions.     

Noncentral matrix quadratic forms of the skew elliptical variables

In this paper, the noncentral matrix quadratic forms of the skew elliptical variables are studied. A family of the matrix variate noncentral generalized Dirichlet distributions is introduced as the extension of the noncentral Wishart distributions, the Dirichlet distributions and the noncentral generalized Dirichlet distributions. Main distributional properties are investigated. These include probability density and closure property under linear transformation and marginalization, the joint distribution of the sub-matrices of the matrix quadratic forms in the skew elliptical variables and the moment generating functions and Bartlett's decomposition of the matrix quadratic forms in the skew normal variables. Two versions of the noncentral Cochran's Theorem for the matrix variate skew normal distributions are obtained, providing sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the matrix variate noncentral generalized Dirichlet distributions. Applications include the properties of the least squares estimation in multivariate linear model and the robustness property of the Wilk's likelihood ratio statistic in the family of the matrix variate skew elliptical distributions.     

微极热弹性无限板的轴对称自由振动

研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.     

Noncentral quadratic forms of the skew elliptical variables

In this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution.