# randomgen.mtrand.RandomState.standard_gamma¶

- RandomState.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.

- Parameters
**shape**float or array_like of floatsParameter, must be non-negative.

**size**int or tuple of ints, optionalOutput 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.

- Returns
**out**ndarray or scalarDrawn 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

\[p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},\]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.

References

- 1
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. https://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., 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()