NAG FL Interface
g05rgf (copula_​plackett_​bivar)

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1 Purpose

g05rgf generates pseudorandom uniform bivariates with joint distribution of a Plackett copula.

2 Specification

Fortran Interface
Subroutine g05rgf ( n, theta, sorder, state, x, ldx, sdx, ifail)
Integer, Intent (In) :: n, sorder, ldx, sdx
Integer, Intent (Inout) :: state(*), ifail
Real (Kind=nag_wp), Intent (In) :: theta
Real (Kind=nag_wp), Intent (Inout) :: x(ldx,sdx)
C Header Interface
#include <nag.h>
void  g05rgf_ (const Integer *n, const double *theta, const Integer *sorder, Integer state[], double x[], const Integer *ldx, const Integer *sdx, Integer *ifail)
The routine may be called by the names g05rgf or nagf_rand_copula_plackett_bivar.

3 Description

Generates pseudorandom uniform bivariates {u1,u2}[0,1]2 whose joint distribution is the Plackett copula Cθ with parameter θ, given by
Cθ = [1+(θ-1)(u1+u2)] - [1+(θ-1)(u1+u2)] 2 - 4 u1 u2 θ (θ-1) 2(θ-1) ,   θ (0,) {1}  
with the special cases:
The generation method uses conditional sampling.
One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05rgf.

4 References

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

5 Arguments

1: n Integer Input
On entry: n, the number of bivariates to generate.
Constraint: n0.
2: theta Real (Kind=nag_wp) Input
On entry: θ, the copula parameter.
Constraint: theta0.0.
3: sorder Integer Input
On entry: determines the storage order of variates; the (i,j)th variate is stored in x(i,j) if sorder=1, and x(j,i) if sorder=2, for i=1,2,,n and j=1,2.
Constraint: sorder=1 or 2.
4: state(*) Integer array Communication Array
Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
5: x(ldx,sdx) Real (Kind=nag_wp) array Output
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 sorder=1 and the jth value for the ith dimension if sorder=2.
6: ldx Integer Input
On entry: the first dimension of the array x as declared in the (sub)program from which g05rgf is called.
Constraints:
  • if sorder=1, ldxn;
  • if sorder=2, ldx2.
7: sdx Integer Input
On entry: the second dimension of the array x as declared in the (sub)program from which g05rgf is called.
Constraints:
  • if sorder=1, sdx2;
  • if sorder=2, sdxn.
8: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
ifail=1
On entry, corrupt state argument.
ifail=2
On entry, invalid theta: theta=value.
Constraint: theta0.0.
ifail=3
On entry, n=value.
Constraint: n0.
ifail=4
On entry, invalid sorder.
Constraint: sorder=1 or 2.
ifail=6
On entry, ldx must be at least value: ldx=value.
ifail=7
On entry, sdx must be at least value: sdx=value.
ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
ifail=-399
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
ifail=-999
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g05rgf 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 routine. 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 x02amf; and ε is the machine precision returned by x02ajf.

10 Example

This example generates thirteen variates for copula C2.0.

10.1 Program Text

Program Text (g05rgfe.f90)

10.2 Program Data

Program Data (g05rgfe.d)

10.3 Program Results

Program Results (g05rgfe.r)