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Statistical Dependence: Copula Functions and Mutual Information Based Measures |
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PP: 1-14 |
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Author(s) |
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Pranesh Kumar,
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Abstract |
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| Accurately and adequately modeling and analyzing relationships in
real random phenomena involving several variables are prominent
areas in statistical data analysis. Applications of such models are
crucial and lead to severe economic and financial implications in
human society. Since the beginning of developments in Statistical
theory as the formal scientific discipline, correlation based
regression theories have played a vital role in understanding and
analyzing multivariate relationships primarily in context of the
normal distribution world and under the assumption of linear
association. In this paper, we aim to focus on presenting notion of
dependence of random variables in statistical sense and mathematical
requirements of dependence measures. We consider copula functions
and mutual information which are employed to characterize
dependence. Some results on copulas and mutual information as
measure of dependence are presented and illustrated using real
examples. We conclude by discussing some possible research question
and by listing the important contributions in this area.
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