NAG FL Interface
g05shf (dist_​f)

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1 Purpose

g05shf generates a vector of pseudorandom numbers taken from an F (or Fisher's variance ratio) distribution with μ and ν degrees of freedom.

2 Specification

Fortran Interface
Subroutine g05shf ( n, df1, df2, state, x, ifail)
Integer, Intent (In) :: n, df1, df2
Integer, Intent (Inout) :: state(*), ifail
Real (Kind=nag_wp), Intent (Out) :: x(n)
C Header Interface
#include <nag.h>
void  g05shf_ (const Integer *n, const Integer *df1, const Integer *df2, Integer state[], double x[], Integer *ifail)
The routine may be called by the names g05shf or nagf_rand_dist_f.

3 Description

The distribution has PDF (probability density function)
f (x) = ( μ+ν-2 2 ) ! x 12 μ-1 (12μ-1)! (12ν-1) ! (1+μνx) 12 (μ+ν) × (μν) 12μ if ​ x>0 , f(x)=0 otherwise.  
g05shf calculates the values
ν yi μ zi ,   i=1,2,,n ,  
where yi and zi are generated by g05sjf from gamma distributions with parameters (12μ,2) and (12ν,2) respectively (i.e., from χ2-distributions with μ and ν degrees of freedom).
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 g05shf.

4 References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5 Arguments

1: n Integer Input
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2: df1 Integer Input
On entry: μ, the number of degrees of freedom of the distribution.
Constraint: df11.
3: df2 Integer Input
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df21.
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(n) Real (Kind=nag_wp) array Output
On exit: the n pseudorandom numbers from the specified F-distribution.
6: 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:
On entry, n=value.
Constraint: n0.
On entry, df1=value.
Constraint: df11.
On entry, df2=value.
Constraint: df21.
On entry, state vector has been corrupted or not initialized.
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.
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g05shf 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

The time taken by g05shf increases with μ and ν.

10 Example

This example prints five pseudorandom numbers from an F-distribution with two and three degrees of freedom, generated by a single call to g05shf, after initialization by g05kff.

10.1 Program Text

Program Text (g05shfe.f90)

10.2 Program Data

Program Data (g05shfe.d)

10.3 Program Results

Program Results (g05shfe.r)