nag_rand_chi_sq (g05sdc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rand_chi_sq (g05sdc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_chi_sq (g05sdc) generates a vector of pseudorandom numbers taken from a χ2-distribution with ν degrees of freedom.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_chi_sq (Integer n, Integer df, Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx = x ν/2-1 × e -x/2 2 ν/2 × ν/2-1 ! if ​ x>0 ; fx=0 otherwise.
This is the same as a gamma distribution with parameters ν/2 and 2.
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_chi_sq (g05sdc).

4  References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
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:     dfIntegerInput
On entry: ν, the number of degrees of freedom of the distribution.
Constraint: df1 .
3:     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.
4:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified χ2-distribution.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, df=value.
Constraint: df1.
On entry, n=value.
Constraint: n0.
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.
On entry, state vector has been corrupted or not initialized.

7  Accuracy

Not applicable.

8  Further Comments

The time taken by nag_rand_chi_sq (g05sdc) increases with ν.

9  Example

This example prints five pseudorandom numbers from a χ2-distribution with five degrees of freedom, generated by a single call to nag_rand_chi_sq (g05sdc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05sdce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05sdce.r)

nag_rand_chi_sq (g05sdc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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