Generates pseudorandom numbers from a standard gamma distribution.

Synopsis

#include <imsl.h>

float *imsl_f_random_gamma (int n_random, float a, ¼, 0)

The type double procedure is imsl_d_random_gamma.

Required Arguments

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

float a   (Input)
The shape parameter of the gamma distribution. This parameter must be positive.

Return Value

If no optional arguments are used, imsl_f_random_gamma returns a pointer to a vector of length n_random containing the random standard gamma deviates. To release this space, use free.

Synopsis with Optional Arguments

#include <imsl.h>

float *imsl_f_random_gamma (int n_random, float a,
IMSL_RETURN_USER, float r[],
0)

Optional Arguments

IMSL_USER_RETURN, float r[]   (Output)
If specified, the vector of length n_random containing the random standard gamma deviates is returned in the user-provided array r.

Description

The function imsl_f_random_gamma generates pseudorandom numbers from a gamma distribution with shape parameter a and unit scale parameter. The probability density function is

Various computational algorithms are used depending on the value of the shape parameter a. For the special case of a = 0.5, squared and halved normal deviates are used; and for the special case of a = 1.0, exponential deviates are generated. Otherwise, if a is less than 1.0, an acceptance-rejection method due to Ahrens, described in Ahrens and Dieter (1974), is used. If a is greater than 1.0, a ten-region rejection procedure developed by Schmeiser and Lal (1980) is used.

Deviates from the two-parameter gamma distribution with shape parameter a and scale parameter b can be generated by using imsl_f_random_gamma and then multiplying each entry in r by b. The following statements (in single precision) would yield random deviates from a gamma (a, b) distribution.

float *r;
r = imsl_f_random_gamma(n_random, a, 0);
for (i=0; i<n_random; i++) *(r+i) *= b;

The Erlang distribution is a standard gamma distribution with the shape parameter having a value equal to a positive integer; hence, imsl_f_random_gamma generates pseudorandom deviates from an Erlang distribution with no modifications required.

The function imsl_random_seed_set can be used to initialize the seed of the random number generator. The function imsl_random_option can be used to select the form of the generator.

Example

In this example, imsl_f_random_gamma is used to generate five pseudorandom deviates from a gamma (Erlang) distribution with shape parameter equal to 3.0.

#include <imsl.h>

void main()
{
    int         seed = 123457;
    int         n_random = 5;
    float       a = 3.0;
    float       *r;

    imsl_random_seed_set(seed);
    r = imsl_f_random_gamma(n_random, a, 0);
    imsl_f_write_matrix("Gamma(3) random deviates", 1, n_random, r, 0);
}

Output

            Gamma(3) random deviates
    1           2           3           4           5
6.843       3.445       1.853       3.999       0.779

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