`numpy.random._generator:Generator.weibull`

Signature

def weibull ( a , size = None )

Summary

Draw samples from a Weibull distribution.

Extended Summary

Draw samples from a 1-parameter Weibull distribution with the given shape parameter a.

X = (- l n (U))^{1/ a}

Here, U is drawn from the uniform distribution over (0,1].

The more common 2-parameter Weibull, including a scale parameter $λ$ is just $X = λ (- l n (U))^{1/ a}$ .

Parameters

a : float or array_like of floats: Shape parameter of the distribution. Must be nonnegative.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if a is a scalar. Otherwise, np.array(a).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized Weibull distribution.

Notes

The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions.

The probability density for the Weibull distribution is

p (x) = \frac{a}{λ} (\frac{x}{λ})^{a - 1} e^{- (x / λ)^{a}},

where $a$ is the shape and $λ$ the scale.

The function has its peak (the mode) at $λ (\frac{a - 1}{a})^{1/ a}$ .

When a = 1, the Weibull distribution reduces to the exponential distribution.

Examples

Draw samples from the distribution:

rng = np.random.default_rng()
a = 5. # shape
s = rng.weibull(a, 1000)

✓

Display the histogram of the samples, along with the probability density function:

import matplotlib.pyplot as plt
def weibull(x, n, a):
    return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)
count, bins, _ = plt.hist(rng.weibull(5., 1000))
x = np.linspace(0, 2, 1000)
bin_spacing = np.mean(np.diff(bins))

✓

plt.plot(x, weibull(x, 1., 5.) * bin_spacing * s.size, label='Weibull PDF')
plt.legend()

✗

plt.show()

✓

Aliases

numpy.random.Generator.weibull