A class of models for uncorrelated random variables
A class of models for uncorrelated random variables
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DOI：
10.1016/j.jmva.2010.03.011
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发表时间：
2010-09-01
影响因子：
1.6
通讯作者：
Volkmer, Hans
中科院分区：
文献类型：
--
作者：
Ebrahimi, Nader;Hamedani, G. G.;Volkmer, Hans
我们考虑一类多元分布，它给出了不相关随机变量之和的分布，由它们的边际分布的乘积给出。这个类是由子独立性的假设的表示定义的，以前在特征函数和卷积方面制定的，作为一个比随机变量和的分布的推导的独立性更弱的假设。新的表示是在随机等价和类的分布被称为可和不相关边际（SUM）分布。SUM分布可以用作不相关随机变量的联合分布的模型，而不管它们之间的依赖强度如何。通过连接任意一对相同的对称概率密度函数，给出了构造二元SUM分布的一种方法。我们还给出了衡量SUM模型相关强度的公式。最后的结果表明，在正相关或负相关的条件下，SUM性质隐含着独立性。(C)2010年爱思唯尔公司All rights reserved.
We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence. (C) 2010 Elsevier Inc. All rights reserved.