nag_rngs_f (g05ldc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rngs_f (g05ldc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_f (g05ldc) 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>
#include <nagg05.h>
void  nag_rngs_f (Integer df1, Integer df2, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx= μ+ν-22 ! x12μ-1 12μ-1! 12ν-1! 1+μνx 12μ+ν × μν 12μ if ​x>0, fx=0 otherwise.
nag_rngs_f (g05ldc) calculates the values
ν yi μ zi ,   i= 1,,n,
where yi and zi are generated by nag_rngs_gamma (g05lfc) 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 nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_f (g05ldc).

4  References

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

5  Arguments

1:     df1IntegerInput
On entry: μ, the number of degrees of freedom of the distribution.
Constraint: df11.
2:     df2IntegerInput
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df21.
3:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
4:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified F-distribution.
5:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
6:     iseed[4]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.

7  Accuracy

Not applicable.

8  Further Comments

The time taken by nag_rngs_f (g05ldc) increases with μ and ν.

9  Example

This example prints five pseudorandom numbers from an F-distribution with two and three degrees of freedom, generated by a single call to nag_rngs_f (g05ldc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05ldce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05ldce.r)


nag_rngs_f (g05ldc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012