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

copula_clayton generates pseudorandom uniform variates with joint distribution of a Clayton/Cook–Johnson Archimedean copula.

For full information please refer to the NAG Library document for g05rh


, the number of pseudorandom uniform variates to generate.


, the number of dimensions.


, the copula parameter.


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().

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 .

(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 .


Generates pseudorandom uniform -variates whose joint distribution is the Clayton/Cook–Johnson Archimedean copula , given by

with the special case:

, 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_clayton.


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