The Gaussian copula
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The Gaussian copula is the copula that underlies the
multivariate normal distribution.
Copula name

Gaussian copula

Common notation


Parameters

, a
nonnegative definite matrix, i.e. a matrix that
can correspond to a correlation matrix

Domain


Copula

where is
the inverse normal
function and is
the cumulative distribution function of the multivariate normal distribution
defined by a covariance matrix equal to

Kendall’s rank
correlation coefficient (for bivariate case),

Where is the correlation
coefficient between the two variables

Coefficient of upper
tail dependence,

(unless the
correlation matrix exhibits perfect positive or negative dependence)

Coefficient of lower tail
dependence,

(unless the
correlation matrix exhibits perfect positive or negative dependence)

Other comments

The Spearman rank
correlation coefficient is given by:
where is the (normal) correlation coefficient
between the two variables.
If (the
identity
matrix) then we obtain the independence copula.

Nematrian web functions
Functions relating to the above distribution in the two
dimensional case may be accessed via the Nematrian
web function library by using a DistributionName of “Gaussian Copula
(2d)”. For details of other supported probability distributions see here.
NAVIGATION LINKS
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