# naginterfaces.library.rand.copula_​students_​t¶

naginterfaces.library.rand.copula_students_t(mode, n, df, c, comm, statecomm)[source]

copula_students_t sets up a reference vector and generates an array of pseudorandom numbers from a Student’s copula with degrees of freedom and covariance matrix .

For full information please refer to the NAG Library document for g05rc

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/g05/g05rcf.html

Parameters
modeint

A code for selecting the operation to be performed by the function.

Set up reference vector only.

Generate variates using reference vector set up in a prior call to copula_students_t.

Set up reference vector and generate variates.

nint

, the number of random variates required.

dfint

, the number of degrees of freedom of the distribution.

cfloat, array-like, shape

Matrix which, along with , defines the covariance of the distribution. Only the upper triangle need be set.

commdict, communication object, modified in place

Communication structure for the reference vector.

If , this argument must have been initialized by a prior call to copula_students_t.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns
xNone or float, ndarray, shape

The array of values from a multivariate Student’s copula, with holding the th dimension for the th variate.

Raises
NagValueError
(errno )

On entry, .

Constraint: , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the covariance matrix is not positive semidefinite to machine precision.

(errno )

is not the same as when [‘r’] was set up in a previous call.

Previous value of and .

(errno )

On entry, [‘state’] vector has been corrupted or not initialized.

Notes

The Student’s copula, , is defined by

where is the number of dimensions, is the multivariate Student’s density function with degrees of freedom, mean zero and covariance matrix and is the inverse of the univariate Student’s density function with degrees of freedom, zero mean and variance .

multivar_students_t() is used to generate a vector from a multivariate Student’s distribution and stat.prob_students_t is used to convert each element of that vector into a uniformly distributed value between zero and one.

One of the initialization functions init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to copula_students_t.

References

Nelsen, R B, 1998, An Introduction to Copulas. Lecture Notes in Statistics 139, Springer

Sklar, A, 1973, Random variables: joint distribution functions and copulas, Kybernetika (9), 499–460