NAG CL Interface
g05rec (copula_​clayton_​bivar)

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1 Purpose

g05rec generates pseudorandom uniform bivariates with joint distribution of a Clayton/Cook–Johnson Archimedean copula.

2 Specification

#include <nag.h>
void  g05rec (Nag_OrderType order, Integer state[], double theta, Integer n, double x[], Integer pdx, Integer sdx, NagError *fail)
The function may be called by the names: g05rec, nag_rand_copula_clayton_bivar or nag_rand_bivariate_copula_clayton.

3 Description

Generates pseudorandom uniform bivariates {u1,u2}(0,1]2 whose joint distribution is the Clayton/Cook–Johnson Archimedean copula Cθ with parameter θ, given by
Cθ = [max( u1 -θ + u2 -θ -1 ,0)] -1/θ ,   θ (−1,) {0}  
with the special cases:
The generation method uses conditional sampling.
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 g05rec.

4 References

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

5 Arguments

1: order Nag_OrderType Input
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 order=Nag_RowMajor. 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.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: state[dim] Integer Communication Array
Note: the dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
3: theta double Input
On entry: θ, the copula parameter.
Constraint: theta-1.0.
4: n Integer Input
On entry: n, the number of bivariates to generate.
Constraint: n0.
5: x[pdx×sdx] double Output
Note: where X(i,j) appears in this document, it refers to the array element x[(j-1)×pdx+i-1].
On exit: the n bivariate uniforms with joint distribution described by Cθ, with X(i,j) holding the ith value for the jth dimension if order=Nag_ColMajor and the jth value for the ith dimension if order=Nag_RowMajor.
6: pdx Integer Input
On entry: the stride separating matrix row elements in the array x.
  • if order=Nag_ColMajor, pdxn;
  • if order=Nag_RowMajor, pdx2.
7: sdx Integer Input
On entry: the secondary dimension of X.
  • if order=Nag_ColMajor, sdx2;
  • if order=Nag_RowMajor, sdxn.
8: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
On entry, pdx must be at least value: pdx=value.
On entry, sdx must be at least value: sdx=value.
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.
On entry, corrupt state argument.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, invalid theta: theta=value.
Constraint: theta-1.0.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g05rec 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.

9 Further Comments

In practice, the need for numerical stability restricts the range of θ such that: where εs is the safe-range parameter, the value of which is returned by X02AMC; and ε is the machine precision returned by X02AJC.

10 Example

This example generates thirteen variates for copula C-0.8.

10.1 Program Text

Program Text (g05rece.c)

10.2 Program Data


10.3 Program Results

Program Results (g05rece.r)