The t copula
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The t copula is the copula that underlies the
multivariate Student’s t distribution.
Copula name

t copula

Common notation


Parameters

, a nonnegative
definite matrix, i.e. a matrix that can
correspond to a correlation matrix
= degrees of
freedom (, usually is an integer
although in some situations a nonintegral can arise)
(note in principle
each marginal distribution could in principle have a different number of
degrees of freedom although such a refinement is not commonly seen)

Domain


Copula

where is
the inverse student’s
t function and is
the cumulative distribution function of the multivariate student’s t
distribution with arbitrary mean and matrix generator equal to

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

Where is the correlation coefficient
between the two variables

Coefficient of upper
tail dependence,


Coefficient of lower
tail dependence,


Other comments

If (the
identity
matrix) then, in contrast to the Gaussian copula, we
do not recover the independence copula.

Nematrian web functions
Functions relating to the above distribution in the twodimensional
case may be accessed via the Nematrian
web function library by using a DistributionName of “student’s t (2d)”.
For details of other supported probability distributions see here.
NAVIGATION LINKS
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