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bundles / numpy latest / numpy / random / RandomState / weibull

cython_function_or_method

numpy.random:RandomState.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.

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

The more common 2-parameter Weibull, including a scale parameter is just .

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

where is the shape and the scale.

The function has its peak (the mode) at .

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

Examples

Draw samples from the distribution: 
a = 5. # shape
s = np.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(np.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)
✗
plt.show()
✓
fig-a4ced85237aa758d.png

See also

gumbel
random.Generator.weibull

which should be used for new code.

scipy.stats.genextreme
scipy.stats.weibull_max
scipy.stats.weibull_min

Aliases

  • numpy.random.weibull
  • numpy.random.RandomState.weibull