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.     

二元Marshall-Olkin型指数分布的独立性和不相关性

若（X,Y）服从二元Marshall-Olkin型指数分布,则X,Y相互独立与不相关是等价的．     

二元Weinman型指数分布的特征及其应用

导出了Weinman型二元指数分布的一个特征,由此获得了参数θj(j=0,1)的最大似然估计及矩估计,给出了二元Weinman型指数分布的二种模拟,还得到了强度为二元Weinman分布时并联结构系统可靠度的估计.     

Bivariate distributions via a Pareto conditional distribution and a regression function

Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.     

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??Kundu and Gupta proposed to use the importance sampling method to compute the Bayesian estimation of the unknown parameters of the Marshall-Olkin bivariate Weibull distribution. However, we find that the performance of the importance sampling method becomes worse as the sample size gets larger. In this paper, we introduce latent variables to simplify the likelihood function, and use MCMC algorithm to estimate the unknown parameters. Numerical simulations are carried out to assess the performance of the proposed method by comparing with the maximum likelihood estimation, and we find that the Bayesian estimates perform better even for the case of small sample size. A real data is also analyzed for illustrative purpose.     

离散二元几何分布串联系统的参数估计

本文首次给出了二元几何分布的定义及其主要性质,并针对二元几何分布串联系统给出了参数的矩估计和极大似然估计,同时通过大量Monte-Carlo模拟考察了估计的精度,文章最后通过Monte-Carlo数值例子来说明方法的运用.     

二元Block-Basu型指数分布的独立性与不相关性

若（X,Y）服从二元Block-Basu型指数分布,则X,Y相互独立与不相关是等价的．还给出了X,Y的相关系数和尾部相关系数．     

二元混合型索赔分布的复合模型的递推方程

杨静平，程士宏，吴芹(2002)最近给出了索赔额服从一元混合型分布的复合模型的递推公式．本文则将其结果推广到二元情形．并把我们的结果应用于超额赔款再保险实务中．     

二元极值分布混合模型的矩估计

极值理论在各个领域得到了越来越多的关注和应用, 尤其是多元极值分布. 而矩估计是一种经典的参数估计方法, 计算简单且具有某些优良性, 本文给出边缘为标准指数分布的二元极值混合模型相关参数的矩估计及其渐近方差. 并将其与极大似然估计的渐近方差比较, 结果表明矩估计是一个较好的估计.     

Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution

In this paper the problem of estimating the ratio of variances, , in a bivariate normal distribution with unknown mean is considered from a decision-theoretic point of view. First, the UMVU estimator of is derived, and then it is shown to be inadmissible under two specific loss functions, namely, the squared error loss and the entropy loss. The derivation of the results is done by conditioning on an auxiliary negative binomial random variable.     

Number of Records in a Bivariate Sample with Application to Missouri River Flood Data

For a sequence of observations from a bivariate absolutely continuous distribution, two types of records are considered depending on whether a univariate record is established in both or in at least one of the components. The distributional properties of the associated univariate and bivariate record indicators are examined. Correlation between the number of component records and the first two moments of the number of bivariate records in a finite random sample are obtained. These are evaluated for the Farlie-Gumbel-Morgenstern and bivariate normal distributions. Large sample properties of these moments are explored. Our results are used to predict the number of record annual floods at two sites along the Missouri river during the next 50 years.     

Estimation of a Bivariate Extreme Value Distribution

Several threshold methods have been proposed for the purpose of estimating a bivariate extreme value distribution from a sample of data whose distribution is only in its domain of attraction. An integrated view of these methods is presented which leads to the introduction of a new asymptotically consistent estimator of the dependence function characterizing the extreme dependence structure. Through Monte Carlo simulations, the new estimator is also shown to do as well as its competitors and to outperform them in cases of weak dependence. To the authors' knowledge, this is the first time that the small-sample behavior of nonparametric bivariate threshold methods has ever been investigated.     

一类二元有理插值的存在性问题

利用二元Lagrange插值公式对一类二元有理插值函数的存在性给出了一个判别方法,并在判别出该二元有理插值函数存在时,给出了它的表现公式。此外,对导致二元有理插值函数不存在的不可达点,本文给出了一种处理方法,使之由不可达点变成可达点。文章的最后还给出若干数值例子说明了本方法的有效性.     

Robustness to nonnormality of some transformations of the sample correlation coefficient

In this paper, some of the familiar transformations of r are examined for their robustness to nonnormality. General results are given for any parent population f(x, y) and any general transformation g(r) of r. Two types of parent populations are considered for exemplification: The bivariate Edgeworth series distribution and the truncated bivariate normal distribution. The effects of nonnormality are assessed through the parameters μ′₁, μ₂, γ₁, γ₂. Tables are provided comparing these quantities against their bivariate normal counterparts.     

二维正态分布的假设检验

将二维随机向量分解成互不相关的主成分,通过对两主成分的正态独立性检验达到二维随机向量正态性检验的目的.     

Making Use of Incomplete Observations for Regression in Bivariate Normal Model

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.     

二元二次函数逼近的存在性和局部性

This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Pade form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.     

介绍一种二元阈值方法在股票指数上的应用

二元极值的阈值方法的一个发展是用来考虑两个变量的联合分布。这个方法是建立在二元极值的点过程表示法的基础上。本文用参数 (Logistic模型 )和非参数模型对 1992 1999年的上海、深圳日收盘指数对数收益进行分析并给出分析结果。     

二元Block～Basu型指数分布的特征及其应用

导出了二元Block~Basu型指数分布的一个特征,利用该特征,获得了二元Block~Basu型指数分布参数的最大似然估计及矩估计,给出了强度服从二元Block~Basu型分布时并联结构系统可靠度的估计,并给出了二元Block~Basu型指数分布的一个随机模拟.     

一类二元有理插值函数的存在性及算法

文[3]构造了对于矩形网格上基于二元Newton插值公式的一类二元有理插值函数,并给出了其存在性的充分条件.本文进一步证明了这类二元有理插值函数存在性的必要条件,特别地,当m=n时,给出了具有三角形结构的系数矩阵的判别方法,该方法计算简便且具有承袭性,文章最后给出的实例说明了方法的有效性.