brainpy.math.random.weibull(a, size=None, key=None)[source]#

Draw samples from a Weibull distribution.

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

\[X = (-ln(U))^{1/a}\]

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

The more common 2-parameter Weibull, including a scale parameter \(\lambda\) is just \(X = \lambda(-ln(U))^{1/a}\).


New code should use the weibull method of a default_rng() instance instead; please see the random-quick-start.

  • 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.


out – Drawn samples from the parameterized Weibull distribution.

Return type:

ndarray or scalar


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

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

where \(a\) is the shape and \(\lambda\) the scale.

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

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



Draw samples from the distribution:

>>> a = 5. # shape
>>> s = brainpy.math.random.weibull(a, 1000)

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

>>> import matplotlib.pyplot as plt
>>> x = np.arange(1,100.)/50.
>>> def weib(x,n,a):
...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)
>>> count, bins, ignored = plt.hist(brainpy.math.random.weibull(5.,1000))
>>> x = np.arange(1,100.)/50.
>>> scale = count.max()/weib(x, 1., 5.).max()
>>> plt.plot(x, weib(x, 1., 5.)*scale)