NAG CL Interface
g05shc (dist_​f)

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1 Purpose

g05shc 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

#include <nag.h>
void  g05shc (Integer n, Integer df1, Integer df2, Integer state[], double x[], NagError *fail)
The function may be called by the names: g05shc, nag_rand_dist_f or nag_rand_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.  
g05shc calculates the values
ν yi μ zi ,   i=1,2,,n ,  
where yi and zi are generated by g05sjc 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 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 g05shc.

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[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.
5: x[n] double Output
On exit: the n pseudorandom numbers from the specified F-distribution.
6: 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

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, df1=value.
Constraint: df11.
On entry, df2=value.
Constraint: df21.
On entry, n=value.
Constraint: n0.
NE_INTERNAL_ERROR
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.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g05shc 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

The time taken by g05shc 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 g05shc, after initialization by g05kfc.

10.1 Program Text

Program Text (g05shce.c)

10.2 Program Data

None.

10.3 Program Results

Program Results (g05shce.r)