`numpy.random:RandomState.standard_gamma`

Signature

def standard_gamma ( shape , size = None )

Summary

Draw samples from a standard Gamma distribution.

Extended Summary

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

Parameters

shape : float or array_like of floats: Parameter, must be non-negative.
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. 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 scalar: Drawn samples from the parameterized standard gamma distribution.

Notes

The probability density for the Gamma distribution is

p (x) = x^{k - 1} \frac{e ^{- x / θ}}{θ ^{k} Γ ( k )},

where $k$ is the shape and $θ$ the scale, and $Γ$ 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.

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
count, bins, ignored = plt.hist(s, 50, density=True)
plt.show()

✓

Aliases

numpy.random.standard_gamma
numpy.random.RandomState.standard_gamma

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases