nag_rand_chi_sq (g05sdc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, df=value.
Constraint: df1.
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_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

None.

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