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### The t copula

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.