Correlation

::This article is about the correlation coefficient between two random variables. The term correlation can also mean the cross-correlation of two functions or electron correlation in molecular systems.

Copulas and correlation

Usually people think that the information given by a correlation coefficient is enough to define the dependence structure between random variables. This is a popular and erroneous idea. To fully capture the dependence between random variables we must consider the copula between them. The correlation coefficient defines completely the dependence structure only in very particular cases, for example when elliptic cumulative distribution functions are used (this case includes for example the multivariate normal distribution).

Related Topics:
Copula - Cumulative distribution functions - Multivariate normal distribution

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