nag_rand_f (g05shc) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_f (g05shc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_f (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>
#include <nagg05.h>
void  nag_rand_f (Integer n, Integer df1, Integer df2, Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
f x = μ+ν-2 2 ! x 12 μ-1 12 μ-1! 12 ν-1 ! 1+ μν x 12 μ+ν × μν 12μ if ​ x>0 , fx=0 otherwise.
nag_rand_f (g05shc) calculates the values
ν yi μ zi ,   i=1,2,,n ,
where yi and zi are generated by nag_rand_gamma (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 nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_f (g05shc).

4  References

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

5  Arguments

1:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     df1IntegerInput
On entry: μ, the number of degrees of freedom of the distribution.
Constraint: df11.
3:     df2IntegerInput
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df21.
4:     state[dim]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions 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]doubleOutput
On exit: the n pseudorandom numbers from the specified F-distribution.
6:     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.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.

7  Accuracy

Not applicable.

8  Further Comments

The time taken by nag_rand_f (g05shc) 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_rand_f (g05shc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05shce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05shce.r)


nag_rand_f (g05shc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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