Generates pseudorandom numbers from a Weibull distribution.

Synopsis

#include <imsls.h>

float *imsls_f_random_weibull (int n_random, float a, …, 0)

The type double function is imsls_d_random_weibull.

Required Arguments

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

float a   (Input)
Shape parameter of the Weibull distribution. This parameter must be positive.

Return Value

An array of length n_random containing the random deviates of a Weibull distribution.

Synopsis with Optional Arguments

#include <imsls.h>

float *imsls_f_random_weibull (int n_random, float a,
IMSLS_B, float b,
IMSLS_RETURN_USER, float r[],
0)

Optional Arguments

IMSLS_B, float b   (Input)
Scale parameter of the two parameter Weibull distribution.
Default: b = 1.0

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

Description

Function imsls_f_random_weibull generates pseudorandom numbers from a Weibull distribution with shape parameter a and scale parameter b. The probability density function is

for x ≥ 0, a > 0, and b > 0. Function imsls_f_random_weibull uses an antithetic inverse CDF tech­nique to generate a Weibull variate; that is, a uniform random deviate U is generated and the inverse of the Weibull cumulative distribution function is evaluated at 1.0 − U to yield the Weibull deviate.

Note that the Rayleigh distribution with probability density function

for x ≥ 0 is the same as a Weibull distribution with shape parameter a equal to 2 and scale param­eter b equal to

Example

In this example, imsls_f_random_weibull is used to generate five pseudorandom deviates from a two-parameter Weibull distribution with shape parameter equal to 2.0 and scale parameter equal to 6.0—a Rayleigh distribution with the following parameter:

#include <stdio.h>

#include <imsls.h>

 

int main()

{

    int   n_random = 5;

    float a = 3.0;

    float *r;

 

    imsls_random_seed_set(123457);

    r = imsls_f_random_weibull(n_random, a, 0);

    imsls_f_write_matrix("Weibull random deviates:",

        1, n_random, r, IMSLS_NO_COL_LABELS, 0);

}

Output

                 Weibull random deviates:

     0.325       1.104       0.643       0.826       0.552

Warning Errors

IMSLS_SMALL_A                                          The shape parameter is so small that a rel­atively large proportion of the values of deviates from the Weibull cannot be represented.

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