A class of models for uncorrelated random variables |
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Authors: | Nader Ebrahimi GG Hamedani |
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Institution: | a Division of Statistics, Northern Illinois University, DeKalb, IL 60155, United States b Department of Mathematics, Statistics & Computer Science, Marquette University, Milwaukee, WI 53201-1881, United States c Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, P.O. Box 742, Milwaukee, WI 53201, United States d Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, United States |
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Abstract: | 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. |
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Keywords: | 62B10 62E15 62H20 94A17 |
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