The function may be called by the names: g05rhc or nag_rand_copula_clayton.
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 g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05rhc.
Marshall A W and Olkin I (1988) Families of multivariate distributions Journal of the American Statistical Association83 403
Nelsen R B (2006) An Introduction to Copulas (2nd Edition) Springer Series in Statistics
1: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Background information to multithreading can be found in the Multithreading documentation.
g05rhc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
In practice, the need for numerical stability restricts the range of such that:
the function requires ;
if , the function returns pseudorandom uniform variates with joint distribution.
This example generates thirteen four-dimensional variates for copula .