The t copula
[this page | pdf | back links]
The t copula is the copula that underlies the
multivariate Student’s t distribution.
Copula name
|
t copula
|
Common notation
|
|
Parameters
|
, a non-negative
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 non-integral 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 two-dimensional
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
Contents | Prev