standard_gamma(self, shape, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.standard_gamma.
Some inconsistencies with the Dask version may exist.
Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale=1.
New code should use the standard_gamma
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability density for the Gamma distribution is
$$p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},$$where $k$ is the shape and $\theta$ the scale, and $\Gamma$ is the Gamma function.
The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.
Parameter, must be non-negative.
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 shape
is a scalar. Otherwise, np.array(shape).size
samples are drawn.
Drawn samples from the parameterized standard gamma distribution.
Draw samples from a standard Gamma distribution.
Generator.standard_gamma
which should be used for new code.
scipy.stats.gamma
probability density function, distribution or cumulative density function, etc.
Draw samples from the distribution:
This example is valid syntax, but we were not able to check execution>>> shape, scale = 2., 1. # mean and width # doctest: +SKIP
... s = np.random.standard_gamma(shape, 1000000) # 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: +SKIPSee :
... import scipy.special as sps # doctest: +SKIP
... count, bins, ignored = plt.hist(s, 50, density=True) # doctest: +SKIP
... y = bins**(shape-1) * ((np.exp(-bins/scale))/ # doctest: +SKIP
... (sps.gamma(shape) * scale**shape))
... plt.plot(bins, y, linewidth=2, color='r') # doctest: +SKIP
... plt.show() # doctest: +SKIP
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