naginterfaces.library.rand.copula_​gumbel

naginterfaces.library.rand.copula_gumbel(n, m, theta, sorder, statecomm)[source]

copula_gumbel generates pseudorandom uniform variates with joint distribution of a Gumbel–Hougaard Archimedean copula.

For full information please refer to the NAG Library document for g05rk

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g05/g05rkf.html

Parameters
nint

, the number of pseudorandom uniform variates to generate.

mint

, the number of dimensions.

thetafloat

, the copula parameter.

sorderint

Determines the storage order of variates; the th variate is stored in if , and if , for , for .

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
xfloat, ndarray, shape

The pseudorandom uniform variates with joint distribution described by , with holding the th value for the th dimension if and the th value for the th dimension of .

Raises
NagValueError
(errno )

On entry, corrupt [‘state’] argument.

(errno )

On entry, invalid : .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, invalid .

Constraint: or .

Notes

Generates pseudorandom uniform -variates whose joint distribution is the Gumbel–Hougaard Archimedean copula , given by

with the special cases:

, the product copula;

, the Fréchet–Hoeffding upper bound.

The generation method uses mixture of powers.

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_gumbel.

References

Marshall, A W and Olkin, I, 1988, Families of multivariate distributions, Journal of the American Statistical Association (83), 403

Nelsen, R B, 2006, An Introduction to Copulas, (2nd Edition), Springer Series in Statistics