numpy.random.standard_gamma(shape, size=None)

Draw samples from a standard Gamma distribution.

Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.


shape : float

Parameter, should be > 0.

size : int or tuple of ints, optional

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.


samples : ndarray or scalar

The drawn samples.

See also

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


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.


[R265]Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource.
[R266]Wikipedia, “Gamma-distribution”,


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, normed=True)
>>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ \
...                       (sps.gamma(shape) * scale**shape))
>>> plt.plot(bins, y, linewidth=2, color='r')

(Source code)