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
size : tuple of ints
|
---|
See also
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
[95] | 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. |
[96] | Waloddi Weibull, 1951 “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper. |
[97] | 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
>>> def weib(x,n,a):
... return (a/n)*(x/n)**(a-1)*exp(-(x/n)**a)
>>> count, bins, ignored = plt.hist(numpy.random.weibull(5.,1000))
>>> scale = count.max()/weib(x, 1., 5.).max()
>>> x = arange(1,100.)/50.
>>> plt.plot(x, weib(x, 1., 5.)*scale)
>>> plt.show()