NAG Library Function Document

nag_random_normal (g05ddc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

nag_random_normal (g05ddc) returns a pseudorandom real number taken from a Normal (Gaussian) distribution with mean

a

and standard deviation

b

2 Specification

#include <nag.h>

#include <nagg05.h>

double

nag_random_normal (double a, double b)

3 Description

The distribution has PDF (probability density function)

f (x) = \frac{1}{b \sqrt{2 π}} \exp (- \frac{{(x - a)}^{2}}{2 b^{2}}) .

The function uses the method of Brent (1974).

4 References

Brent R P (1974) Algorithm 488 Comm. ACM 704

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: a – doubleInput: On entry: the mean $a$ , of the distribution.
2: b – doubleInput: On entry: the standard deviation $b$ , of the distribution. If b is negative, the distribution of the generated numbers – though not the actual sequence – is the same as if the absolute value of b were used.

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Further Comments

None.

9 Example

The example program prints the first five pseudorandom real numbers from a Normal distribution with mean 1.0 and standard deviation 1.5, generated by nag_random_normal (g05ddc) after initialization by nag_random_init_repeatable (g05cbc).