Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions

We consider here a generalization of the skew-normal distribution, GSN(λ₁,λ₂,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-t_ν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-t_ν form. We then use the relationship between the generalized skew-normal and skew-t_ν distributions to discuss some properties of generalized skew-t_ν as well as distributions of order statistics from bivariate and trivariate t_ν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-t_ν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics.     

Finite normal mixture copulas for multivariate discrete data modeling

A new family of copulas is introduced that provides flexible dependence structure while being tractable and simple to use for multivariate discrete data modeling. The construction exploits finite mixtures of uncorrelated normal distributions. Accordingly, the cumulative distribution function is simply the product of univariate normal distributions. At the same time, however, the mixing operation introduces association. The properties of the new family of copulas are examined and a concrete application is used to show its applicability.     

反思与重构:对结合犯概念的再思考

对结合犯概念的揭示应注意以下几个方面:不能脱离结合犯的初始意义,应反映结合犯的本质内涵和立法目的,不能脱离法律的实证规定,不能混淆规范刑法学与本体刑法学的界限,不能脱离犯罪成立的理论体系.所谓结合犯是指立法者基于特定立法目的的考虑,将两个具有内在联系性的犯罪(构成要件)规定为独立犯罪(构成要件)的情况.     

关于中等师范学校布局调整的思考与实践

中国的改革开放带来的中国社会的高速发展以及知识经济呼之欲出的全球大背景,导致了中等师范学校必须转型的历史命运.中等师范学校如何转型?如何面对新的历史条件下的新情况?中等师范学校只有不等、不靠,积极主动地去思考与探索中师布局的调整,才能走出困境,获得新生.     

高师体育教育改革的研究与实践

通过对中学教师自身健康、体育锻炼和体育能力状况调查研究 ,提出新世纪加强高师体育教育必要性 ,高师体育教育指导思想 ,及加强高师体育教育对策     

综合性大学举办教师教育存在的问题及对策

综合性大学举办的教师教育已经成为我国教师教育的重要组成部分。但目前它仍处于探索阶段,不可避免地存在如下缺陷:学术性和师范性难以兼顾,课程设置有待优化,综合性大学与师范院校缺乏合作,教育专业与非教育专业缺乏双向交流等。要推进综合性大学教师教育的改革与发展,综合性大学可采取如下举措:平衡学术性与师范性,推进教师教育创新;优化教师教育课程设置,促进教师教育课程改革;努力实现资源共享、优势互补,探索教师教育发展道路;加强专业间的合作,促进融合发展。     

师范院校通识教育的实施策略

基于通识教育的内涵和师范教育的特性,师范院校通识教育的使命体现在两个层面:终极层面,即"完整的人"的培养;专业层面,即教育信念的培养。师范院校通识教育在理念、课程、教师、教学方式、教学管理等方面还存在问题。改进和完善师范院校通识教育,必须首先确立科学的通识教育理念,明确通识教育的使命,加强对通识教育理念的宣传;从通识教育的理念和使命出发,顶层设计通识教育课程体系;强化通识教育师资建设,建设一支专、兼结合的优质通识教育课程师资队伍;创新通识教育教学方式,积极推进小班讨论教学、研究型教学,强化经典导课程教学,在专业方向课程教学中融渗通识教育,将专业教育和通识教育有机结合;加强通识教育管理工作,探索建立全校层面的通识教育机构,建立通识教育质量评估反馈机制,建立通识教育课程教学助教制,实施双导师制,推进优质通识教学资源共享。     

The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.     

Bivariate,multivariate, and matrix variate normal characterizations: A brief survey II

The paper entitled “Bivariate and Multivariate Normal Characterizations: A Brief Survey,” by Hamedani, which was published in 1992, covered the published characterizations of bivariate and multivariate normal (MVN) distributions from 1941 to 1991. The present work is a follow-up to the 1991/1992 survey which includes not only characterizations of the bivariate and MVN distributions, but also characterizations of the matrix variate normal distribution, which have appeared from 1991/1992 to the present.     

Construction of bivariate and multivariate weighted distributions via conditioning

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this article, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter, and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real-life data set is used to show the applicability of these bivariate weighted distributions.