Document Type
Article
Language
eng
Format of Original
13 p.
Publication Date
9-2010
Publisher
Elsevier
Source Publication
Journal of Multivariate Analysis
Source ISSN
0047-259X
Original Item ID
doi: 10.1016/j.jmva.2010.03.011
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.
Recommended Citation
Ebrahimi, Nader; Hamedani, Gholamhossein; Soofi, Ehsan S.; and Volkmer, Hans, "A Class of Models for Uncorrelated Random Variables" (2010). Mathematics, Statistics and Computer Science Faculty Research and Publications. 9.
https://epublications.marquette.edu/mscs_fac/9
Comments
Accepted version. Journal of Multivariate Analysis, Vol. 101, No. 8 (September 2010): 1859-1871. DOI. © 2010 Elsevier. Used with permission.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Multivariate Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Multivariate Analysis, [VOL 101, ISSUE 8, (September 2010)] DOI.