randomWeibull¶

Generates pseudorandom numbers from a Weibull distribution.

Synopsis¶

randomWeibull (nRandom, a)

Required Arguments¶

int nRandom (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 nRandom containing the random deviates of a Weibull distribution.

Optional Arguments¶

b, float (Input)

Scale parameter of the two parameter Weibull distribution.

Default: b = 1.0

Description¶

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

\[f(x) = abx^{a-1} \exp\left(-bx^a\right)\]

for \(x\geq 0\), \(a>0\), and \(b>0\). Function randomWeibull 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

\[r(x) = \frac{1}{\alpha^2} xe^{-\left(x^2/\left(2\alpha^2\right)\right)}\]

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

\[\sqrt{2}\alpha\]

Example¶

In this example, randomWeibull 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:

\[\alpha = 3 \sqrt{2}\]

from numpy import *
from pyimsl.stat.randomWeibull import randomWeibull
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
a = 3.0
randomSeedSet(123457)
r = randomWeibull(n_random, a)
writeMatrix("Weibull random deviates", r, noColLabels=True)

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.