The routine may be called by the names g05rjf or nagf_rand_copula_frank.
Generates pseudorandom uniform -variates whose joint distribution is the Frank Archimedean copula , given by
with the special case:
, the Fréchet–Hoeffding upper bound.
The generation method uses mixture of powers.
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 g05rjf.
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: – IntegerInput
On entry: , the number of pseudorandom uniform variates to generate.
2: – IntegerInput
On entry: , the number of dimensions.
3: – Real (Kind=nag_wp)Input
On entry: , the copula parameter.
4: – IntegerInput
On entry: determines the storage order of variates; the
th variate is stored in if , and if , for and .
5: – Integer arrayCommunication 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.
6: – Real (Kind=nag_wp) arrayOutput
On exit: 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 .
7: – IntegerInput
On entry: the first dimension of the array x as declared in the (sub)program from which g05rjf is called.
if , ;
if , .
8: – IntegerInput
On entry: the second dimension of the array x as declared in the (sub)program from which g05rjf is called.
if , ;
if , .
9: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g05rjf 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.
In practice, the need for numerical stability restricts the range of such that:
the routine requires ;
if , the routine returns pseudorandom uniform variates with joint distribution;
where is the machine precision returned by x02ajf.
This example generates thirteen four-dimensional variates for copula .