numpy.random.
weibull
Draw samples from a Weibull distribution.
Draw samples from a 1-parameter Weibull distribution with the given shape parameter a.
System Message: WARNING/2 (X = (-ln(U))^{1/a} )
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Here, U is drawn from the uniform distribution over (0,1].
The more common 2-parameter Weibull, including a scale parameter
System Message: WARNING/2 (\lambda)
System Message: WARNING/2 (X = \lambda(-ln(U))^{1/a})
Note
New code should use the weibull method of a default_rng() instance instead; see random-quick-start.
default_rng()
Shape parameter of the distribution. Must be nonnegative.
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.
(m, n, k)
m * n * k
None
a
np.array(a).size
Drawn samples from the parameterized Weibull distribution.
See also
scipy.stats.weibull_max, scipy.stats.weibull_min, scipy.stats.genextreme, gumbel
scipy.stats.weibull_max
scipy.stats.weibull_min
scipy.stats.genextreme
gumbel
Generator.weibull
which should be used for new code.
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
System Message: WARNING/2 (p(x) = \frac{a} {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a}, )
where
System Message: WARNING/2 (a)
The function has its peak (the mode) at
System Message: WARNING/2 (\lambda(\frac{a-1}{a})^{1/a})
When a = 1, the Weibull distribution reduces to the exponential distribution.
a = 1
References
Waloddi Weibull, Royal Technical University, Stockholm, 1939 “A Statistical Theory Of The Strength Of Materials”, Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm.
Waloddi Weibull, “A Statistical Distribution Function of Wide Applicability”, Journal Of Applied Mechanics ASME Paper 1951.
Wikipedia, “Weibull distribution”, https://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()
