Draw samples from a standard Gamma distribution.

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 Generator instance instead; please see the Quick start .

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.

See also

probability density function, distribution or cumulative density function, etc.

which should be used for new code.

Notes

The probability density for the Gamma distribution is

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.

References

Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. https://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.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()