nag_rngs_normal (g05lac) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rngs_normal (g05lac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_normal (g05lac) generates a vector of pseudorandom numbers taken from a Normal (Gaussian) distribution with mean μ and variance σ2.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_normal (double xmu, double var, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The distribution has PDF (probability distribution function)
fx=1σ2π exp- x-μ 22σ2 .
nag_rngs_normal (g05lac) uses the Box–Muller method.
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_normal (g05lac).

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:     xmudoubleInput
On entry: μ, the mean of the distribution.
2:     vardoubleInput
On entry: σ2, the variance of the distribution.
Constraint: var0.0.
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 Normal 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, 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_REAL
On entry, var=value.
Constraint: var0.0.

7  Accuracy

The generated numbers conform to a Normal distribution with an accuracy of machine precision.

8  Further Comments

None.

9  Example

This example prints five pseudorandom numbers from a Normal distribution with mean 1.0 and variance 1.5, generated by a single call to nag_rngs_normal (g05lac), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lace.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05lace.r)


nag_rngs_normal (g05lac) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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