method
Generator.
standard_gamma
Draw samples from a standard Gamma distribution.
Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.
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.
(m, n, k)
m * n * k
None
shape
np.array(shape).size
Desired dtype of the result, either ‘d’ (or ‘float64’) or ‘f’ (or ‘float32’). All dtypes are determined by their name. The default value is ‘d’.
Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.
Drawn samples from the parameterized standard gamma distribution.
See also
scipy.stats.gamma
probability density function, distribution or cumulative density function, etc.
Notes
The probability density for the Gamma distribution is
System Message: WARNING/2 (p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, )
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where
System Message: WARNING/2 (k)
System Message: WARNING/2 (\theta)
System Message: WARNING/2 (\Gamma)
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
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html
Wikipedia, “Gamma distribution”, https://en.wikipedia.org/wiki/Gamma_distribution
Examples
Draw samples from the distribution:
>>> shape, scale = 2., 1. # mean and width >>> s = np.random.default_rng().standard_gamma(shape, 1000000)
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()
