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Showing content from https://docs.scipy.org/doc/numpy-1.16.0/reference/generated/numpy.random.weibull.html below:

numpy.random.weibull — NumPy v1.16 Manual

Draw samples from a Weibull distribution.

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 .

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 : 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.

References

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()

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