Generates pseudorandom numbers from a normal, N (μ, σ2), distribution.

Synopsis

#include <imsls.h>

float *imsls_f_random_normal (int n_random, ..., 0)

The type double function is imsls_d_random_normal.

Required Arguments

int n_random   (Input)
Number of random numbers to generate.

Return Value

An array of length n_random containing the random normal deviates.

Synopsis with Optional Arguments

#include <imsls.h>

float *imsls_f_random_normal (int n_random,
IMSLS_MEAN, float mean,
IMSLS_VARIANCE, float variance,
IMSLS_ACCEPT_REJECT_METHOD,
IMSLS_RETURN_USER, float r[],
0)

Optional Arguments

IMSLS_MEAN, float mean   (Input)
Parameter mean contains the mean, μ, of the N(μ, σ2) from which random normal deviates are to be generated.
Default: mean = 0.0

IMSLS_VARIANCE, float variance   (Input)
Parameter variance contains the variance of the N (μ, σ2) from which random nor­mal deviates are to be generated.
Default: variance = 1.0

IMSLS_ACCEPT_REJECT_METHOD
By default, random numbers are generated using an inverse CDF technique. When optional argument IMSLS_ACCEPT_REJECT_METHOD is specified, an acceptance/ rejection method is used instead. See the “Description” section for details about each method.

IMSLS_RETURN_USER, float r[]   (Output)
User-supplied array of length n_random containing the generated random standard normal deviates.

Description

By default, function imsls_f_random_normal generates pseudorandom numbers from a normal (Gaussian) distribution using an inverse CDF technique. In this method, a uniform (0, 1) random deviate is generated. The inverse of the normal distribution function is then evaluated at that point, using the function imsls_f_normal_inverse_cdf (Chapter 11, Probablility Distribution Functions and Inverses).

If optional argument IMSLS_ACCEPT_REJECT_METHOD is specified, function imsls_f_random_normal generates pseudorandom numbers using an acceptance/rejection technique due to Kinderman and Ramage (1976). In this method, the normal density is repre­sented as a mixture of densities over which a variety of acceptance/rejection method due to Marsaglia (1964), Marsaglia and Bray (1964), and Marsaglia et al. (1964) are applied. This method is faster than the inverse CDF technique.

Remarks

Function imsls_random_seed_set can be used to initialize the seed of the random number generator; function imsls_random_option can be used to select the form of the generator.

Example

In this example, imsls_f_random_normal generates five pseudorandom deviates from a standard normal distribution.

#include <imsls.h>
#define N_RANDOM  5

void main()

{

    int         seed = 123457;

    int         n_random = N_RANDOM;

    float       *r;

    imsls_random_seed_set (seed);

    r = imsls_f_random_normal(n_random, 0);

    printf("%s:\n%8.4f%8.4f%8.4f%8.4f%8.4f\n",

           "Standard normal random deviates",

           r[0], r[1], r[2], r[3], r[4]);

}

Output

Standard normal random deviates:

1.8279      -0.6412  0.7266  0.1747  1.0145

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