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.     

基于正则逆Gamma分布和广义极值分布的VaR计算

股指收益率的分布和风险价值(VaR)的计算是证券市场研究的热点问题.本文对来自上证指数和深证成指日收益率采用正则逆Gamma分布和偏T分布(SST)分别进行拟合,对极值序列(周、月极大值和极小值)建立广义极值分布函数。并由此计算VaR值,度量这几种序列的风险价值.结果表明正则逆Gamma分布能更好地拟合日收益率的分布,以及采用周极值收益率的广义极值分布计算VaR值来估计风险较为合理.     

椭球等高分布的逆问题

本文给出了Ｘ１｜Ｘ２＝ｘ２和Ｘ２｜Ｘ１＝ｘ１均为椭球等高分布时,Ｘ１与Ｘ２的联合分布仍为椭球等高分布的充要条件,同时证明了当Ｘ１｜Ｘ２＝ｘ２,Ｙ２均服从椭球等高分布时,Ｘ１与Ｘ２＝ｕ２＋Ｃ１Ｙ２的联合分布为椭球等高分布。     

椭球等高矩阵分布关于非奇异矩阵变换的不变性

本文首先将矩阵F分布和矩阵t分布的定义推广到左球分布类,其密度函数与产生它们的左球分布或球对称分布的密度均无关.然后讨论了椭球等高分布关于非奇异矩阵变换的不变性问题,包括矩阵Beta分布、逆矩阵Beta分布、矩阵Dirichlet分布、逆矩阵Dirichlet分布、矩阵F分布和矩阵t等分布.在非奇异变换下,这些分布的密度不但与产生它们的左球分布的密度函数无关,而且与非奇异变换矩阵无关.     

退化矩阵Liouville,Beta,Dirichlet分布

该文引进和讨论了退化矩阵Liouville分布，由此导出退化矩阵Beta分布、退化矩阵Dirichlet分布．推广了文献［1］关于退化Wishart分布和秩为1的退化矩阵Beta分布的结果。     

P-范分布及其抽样分布

本文构造了n维P-范分布的密度函数，使拉普拉斯分布、正态分布、均匀分布与退化分布均为一维P-范分布的特例。然后，定义了三个与P-范分布有密切关系的抽样分布，并给出了密度函数。     

关于伽马分布及相关分布性质的一点研究

主要研究伽马分布的性质,并通过对伽马分布可加性的研究.得到由指数分布通过伽马分布构造卡方分布和均匀分布的方法,通过本文可以加深对伽马分布和其它常见连续性分布关系的认识.     

一个组合分布模型及其参数估计

本文根据极值分布理论,提出了一个由原始分布和尾分布组成的组合分布模型,研究了组合分布模型中原始分布和尾分布的确定方法,建立了组合分布模型参数估计的加权最优化模型,实例计算说明,组合分布较好地反映了风险变量极值事件的风险。     

基于BG分布的资产收益率分布拟合与尾部风险测度——以上海黄金市场为例

本文以上海黄金市场为例,在GARCH模型下,系统性比较了基于正态分布、Logistic分布、HS分布、Laplace分布、t2分布和Cauchy分布的对称和非对称共12种BG分布在收益率分布拟合以及VaR和ES测度中的效果。研究结果表明,BG分布在收益率分布建模与尾部风险测度上的表现与原分布类型有关。当原分布为正态分布时,对称和非对称BG分布的效果都较差。当原分布为Logistic分布、HS分布、Laplace分布、t2分布和Cauchy分布时,对称和非对称BG分布的效果都较好,其中非对称BG分布效果在尾部分布拟合上优势更大。在所有分布中,基于t2分布和Cauchy分布的非对称BG分布表现最优。     

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。     

Convergence of linear functions of Pfeifer records

The probabilistic behaviour of partial sums of upper and lower records has been studied in the literature. In this article, we take a broader view and study partial sums of record like sequences. We show that such sequences converge in distribution to normal and lognormal distribution. In particular our results apply to Pfeifer records. We also show the strong convergence of partial sums of lower Pfeifer records under suitable assumptions.     

On the Characteristic Properties of Exponential Distribution

New characterizations for the exponential distribution are given in terms of record values and the probabilities of finite sums of independent and identically distributed nonnegative random variables provided that the underlying distribution is either new better than used or new worse than used.     

A Review of Results on Sums of Random Variables

Sums of random variables arise naturally in wireless communications and related areas. Here, we provide a review of the known results on sums of exponential, gamma, lognormal, Rayleigh and Weibull random variables. A discussion is provided of two applications. We expect that this review could serve as a useful reference and help to advance further research in this area.     

Record values in sequences of sample ranges

The classical representation of record values in sequences of independent random variables with the standard exponential distribution E(1) as sums of exponentially distributed random summands plays an important role in the mathematical theory of records. A generalization of this representation is proposed. A new similar result that makes it possible to express the record values of sample ranges as sums of independent exponentially distributed random variables is obtained.     

Asymptotic Properties of Sums of Upper Records

Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results.     

长尾宽上限相依的不同分布的随机变量和的精确大偏差

研究了服从长尾分布族上的随机变量和的精确大偏差问题,其中假设代表索赔额的随机变量序列是一列宽上限相依的、不同分布的随机变量序列。在给定一些假设条件下,得到了部分和与随机和的两种一致渐近结论。     

A mixture-type limit theorem for nonlinear functions of Gaussian sequences

We show that, for a certain class of nonlinear functions of Gaussian sequences, the limiting distribution of normalized sums of the nonlinear function values of a sequence is the convolution of a Gaussian distribution with another non-Gaussian distribution.     

Limiting behavior of weighted sums with stable distributions

We present an integral test to determine the limiting behavior of weighted sums of independent, symmetric random variables with stable distributions, and deduce Chover-type laws of the iterated logarithm for them.     

两类记录值之和的中心极限定理

该文给出了Ｌｏｇｉｓｔｉｃ分布纪录值序列部分和的中心极限定理；对于Ｐａｒｅｔｏ分布纪录值序列的部分和T_n，获得了ｌｎT_n的中心极限定理．这一工作不仅具有概率论的极限理论方面的研究价值，而且在金融、保险等领域也具有相当重要的应用前景．     

Geometric stable laws: Estimation and applications

Geometric stable laws constitute a class of limiting distributions of appropriately normalized random sums of i.i.d. random variables. We consider the problem of estimation of the parameters of univariate and multivariate geometric stable laws. Our estimation technique is based on the method of moments and yields consistent and asymptotically normal estimators. We apply our estimators to a currency exchange data and show that the geometric stable dominates Paretian stable and normal models.