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.     

从SPⅦ分布生成的新的多元偏态t分布的有关性质

随机向量的t分布属于椭球等高分布族,然而,它是对称分布.在许多诸如经济学、生理学、社会学等领域中,有时回归模型中的随机误差不再满足对称性,通常表现出高度的偏态性(skewness).于是就有了偏态椭球等高分布族.本文在已有的多元偏态t分布的基础上,着重研究它的分布性质,包括线性组合分布、边缘分布、条件分布及各阶矩.     

从SPVⅡ分布生成的新的多元偏态t分布的有关性质

随机向量的t分布属于椭球等高分布族,然而,它是对称分布.在许多诸如经济学、生理学、社会学等领域中,有时回归模型中的随机误差不再满足对称性,通常表现出高度的偏态性(skewness).于是就有了偏态椭球等高分布族.本文在已有的多元偏态t分布的基础上,着重研究它的分布性质,包括线性组合分布、边缘分布、条件分布及各阶矩.     

缺失偏t正态数据下线性回归模型的统计推断

本文研究缺失偏t正态数据下线性回归模型的参数估计问题,针对缺失偏t正态数据,为使样本分布更加接近真实分布,改善模型的回归系数、尺度参数、偏度参数和自由度参数的估计效果,提高参数估计的稳定性,提出一种适合缺失偏t正态数据下线性回归模型的修正随机回归插补方法.通过随机模拟和实例研究,同随机回归插补,多重随机回归插补方法比较,结果表明所提出的修正随机回归插补方法是有效可行的.     

偏态自适型投影深度

对常规投影深度进行了改进,得到了一类新的可自适应反映多元数据云偏态的统计投影深度.新的深度函数仍然具有凸的深度域,满足一般统计深度函数所应具备的全部基本特点.此外,还考虑了新投影深度函数的计算问题,证得在任意维空间里,它及由它诱导的深度域均是可以精确计算的,从技术角度讲,其处理比常规投影深度更加简便.最后,提供了一些数据示例用以展示此偏态自适型投影深度的有限样本性质.     

多元t分布的一致渐进正态性

讨论了多元t分布一致渐进正态性的条件,利用不等式法估计了二者之间的Kullback-Leibler距离,给出了Kullback-Leibler距离表达式,最后对多元t分布一致渐进正态性进行了模拟验证.     

带有误差变量的偏度和峰度正态性检验

考虑带有误差变量偏度和峰度正态性检验问题 ,提出了新的偏度和峰度正态性检验统计量 ,证明了在零假设时 ,所提出的偏度和峰度检验统计量具有渐近正态的优良性质     

数理统计学小史

６误差分布：正态与偏态（上）上一章我们讲了最小二乘法及其相关的发展,在那里,这个方法是纯粹作为一个处理测量值的代数方法来讨论的,不涉及有关的统计推断问题,要研究这个问题,需要考虑到测量值有误差。这种误差（假定量测过程排除了可能的系统性因素的影响）是随...     

渐近正态随机变量函数的极限分布

基于渐近正态随机变量,导出随机变量函数极限分布的两个一般性理论结果.作为应用,证明了渐近正态随机变量一系列具体函数的极限分布,其中包括泊松随机变量平方根的渐近正态性,以及随机变量部分和在正则化常数是随机变量情况下的渐近正态性.     

Gamma分布与Beta分布的一致渐近正态性

考虑了Gamma分布与Beta分布的一致渐近正态性.     

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 New Robust Class of Skew Elliptical Distributions

Methodology and Computing in Applied Probability - A new robust class of multivariate skew distributions is introduced. Practical aspects such as parameter estimation method of the proposed class...     

Some Truncated Bivariate Distributions

Truncated versions of the bivariate generalized Pareto, bivariate inverted dirichlet and the bivariate Pearson type VII distributions are introduced. Unlike the un-truncated versions, these possess finite moments of all orders and could therefore be better models for certain practical situations. Explicit expressions for the moments are derived for each of the truncated distribution.     

Bivariate Distributions with Pearson Type VII Conditionals

In this article the most general class of bivariate distributions such that both conditional densities are Pearson Type VII, with fixed shape parameter, is fully characterized. Some of its properties and relations with other distributions are explored. The estimation of parameters is considered by the methods of maximum likelihood and pseudolikelihood and a method for random variate generation is presented along with a simulation experiment. Bivariate and multivariate extensions of the Pearson Type VII conditionals distribution are also discussed.     

一般形式下斜正态随机向量的矩

本文给出一般形式下斜正态随机向量及其平方型的矩公式. 作为应用, 计算出了斜正态随机向量的多元偏度和峰度.     

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.     

Skew Distributions Generated from Different Families

Following the recent paper by Gupta et al. [8], skew pdfs of the form are generated, where the pdf and the cdf are taken to be different and to come from normal, Student's , Cauchy, Laplace, logistic or the uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the th moment and the characteristic function are derived. Graphical illustrations are also provided.     

Variational Inequalities for Arbitrary Multivariate Distributions

Upper bounds for the total variation distance between two arbitrary multivariate distributions are obtained in terms of the correspondingw-functions. The results extend some previous inequalities satisfied by the normal distribution. Some examples are also given.