random_weibull

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 Weibull distribution with shape parameter equal to 3.0.

 

 

#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.