Draw samples from a Gamma distribution.
Samples are drawn from a Gamma distribution with specified parameters,
shape (sometimes designated “k”) and scale (sometimes designated
“theta”), where both parameters are > 0.
Note
New code should use the gamma
method of a default_rng()
instance instead; see random-quick-start.
- Parameters
- shapefloat or array_like of floats
The shape of the gamma distribution. Must be non-negative.
- scalefloat or array_like of floats, optional
The scale of the gamma distribution. Must be non-negative.
Default is equal to 1.
- sizeint 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 shape
and scale
are both scalars.
Otherwise, np.broadcast(shape, scale).size
samples are drawn.
- Returns
- outndarray or scalar
Drawn samples from the parameterized gamma distribution.
Notes
The probability density for the Gamma distribution is
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where
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is the shape and
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the scale,
and
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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.
References
- 1
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A
Wolfram Web Resource.
http://mathworld.wolfram.com/GammaDistribution.html
- 2
Wikipedia, “Gamma distribution”,
https://en.wikipedia.org/wiki/Gamma_distribution
Examples
Draw samples from the distribution:
>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2)
>>> s = np.random.gamma(shape, scale, 1000)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
>>> count, bins, ignored = plt.hist(s, 50, density=True)
>>> y = bins**(shape-1)*(np.exp(-bins/scale) /
... (sps.gamma(shape)*scale**shape))
>>> plt.plot(bins, y, linewidth=2, color='r')
>>> plt.show()