weibull(self, a, size=None, chunks='auto', **kwargs)

This docstring was copied from numpy.random.mtrand.RandomState.weibull.

Some inconsistencies with the Dask version may exist.

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 $X = \lambda(-ln(U))^{1/a}$ .

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

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

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.

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.

Draw samples from a Weibull distribution.

See Also

Generator.weibull

which should be used for new code.

gumbel

scipy.stats.genextreme

scipy.stats.weibull_max

scipy.stats.weibull_min

Examples

Draw samples from the distribution:

This example is valid syntax, but we were not able to check execution

>>> a = 5. # shape  # doctest: +SKIP
... s = np.random.weibull(a, 1000)  # doctest: +SKIP

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

This example is valid syntax, but we were not able to check execution

>>> import matplotlib.pyplot as plt  # doctest: +SKIP
... x = np.arange(1,100.)/50.  # doctest: +SKIP
... def weib(x,n,a):  # doctest: +SKIP
...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)

This example is valid syntax, but we were not able to check execution

>>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))  # doctest: +SKIP
... x = np.arange(1,100.)/50.  # doctest: +SKIP
... scale = count.max()/weib(x, 1., 5.).max()  # doctest: +SKIP
... plt.plot(x, weib(x, 1., 5.)*scale)  # doctest: +SKIP
... plt.show()  # doctest: +SKIP

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

dask.array.random.RandomState.gumbel

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