Generates pseudorandom numbers from a beta distribution.

Synopsis

#include <imsl.h>

float *imsl_f_random_beta (float n_random, float pin, float qin, ¼, 0)

The type double function is imsl_d_random_beta.

Required Arguments

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

float pin   (Input)
First beta distribution parameter. Argument pin must be positive.

float qin   (Input)
Second beta distribution parameter. Argument qin must be positive.

Return Value

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

Synopsis with Optional Arguments

#include <imsl.h>

float *imsl_f_random_beta (float n_random, float pin, float qin,
IMSL_RETURN_USER, float r[],
0)

Optional Arguments

IMSL_RETURN_USER, float r[]   (Output)
If specified, the vector of length n_random containing the random standard beta deviates is returned in r.

Description

The function imsl_f_random_beta generates pseudorandom numbers from a beta distribution with parameters pin and qin, both of which must be positive. With p = pin and q = qin, the probability density function is

where Γ(×) is the gamma function.

The algorithm used depends on the values of p and q. Except for the trivial cases of
p = 1 or q = 1, in which the inverse CDF method is used, all of the methods use acceptance/rejection. If p and q are both less than 1, the method of Jöhnk (1964) is used. If either p or q is less than 1 and the other is greater than 1, the method of Atkinson (1979) is used. If both p and q are greater than 1, algorithm BB of Cheng (1978), which requires very little setup time, is used if n_random is less than 4; and algorithm B4PE of Schmeiser and Babu (1980) is used if n_random is greater than or equal to 4. Note that for p and q both greater than 1, calling imsl_f_random_beta in a loop getting less than 4 variates on each call will not yield the same set of deviates as calling imsl_f_random_beta once and getting all the deviates at once.

The values returned in r are less than 1.0 and greater than ɛ where ɛ is the smallest positive number such that 1.0 − ɛ is less than 1.0.

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_beta is used to generate five pseudorandom beta (3, 2) variates.

#include <imsl.h>

main()
{

    int         n_random = 5;
    int         seed = 123457;
    float       pin = 3.0;
    float       qin = 2.0;
    float       *r;

    imsl_random_seed_set (seed);     
    r = imsl_f_random_beta (n_random, pin, qin, 0);
    imsl_f_write_matrix("Beta (3,2) random deviates", 1, n_random, r, 0);
}

Output

            Beta (3,2) random deviates
     1           2           3           4           5
0.2814      0.9483      0.3984      0.3103      0.8296

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