Copulas in three dimensions with prescribed correlations

Details Copulas in three dimensions with prescribed correlations Copulas in three dimensions with prescribed correlations

2010-04-19

arxiv.org/abs/1004.3146v1

Mathematics

Statistics Theory

15 pages, 2 figures

Scientific paper

Given an arbitrary three-dimensional correlation matrix, we prove that there
exists a three-dimensional joint distribution for the random variable $(X,Y,Z)$
such that $X$,$Y$ and $Z$ are identically distributed with beta distribution
$\beta_{k,k}(dx)$ on $(0,1)$ if $k\geq 1/2$. This implies that any correlation
structure can be attained for three-dimensional copulas.

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