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# numpy.random.mtrand.RandomState.weibull

`RandomState.``weibull`(a, size=None)

  Weibull distribution.

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

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

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

  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.

  Parameters : | a : float Shape of the distribution. size : tuple of ints Output shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn.

  See also

  `scipy.stats.distributions.weibull`
    probability density function, distribution or cumulative density function, etc.

  `gumbel`, `scipy.stats.distributions.genextreme`

  Notes

  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

  [R217] | Waloddi Weibull, Professor, Royal Technical University, Stockholm, 1939 “A Statistical Theory Of The Strength Of Materials”, Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm.

  [R218] | Waloddi Weibull, 1951 “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper.

  [R219] | Wikipedia, “Weibull distribution”, http://en.wikipedia.org/wiki/Weibull_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()

  (Source code, png, pdf)

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