nlcpy.random.RandomState.standard_gamma

RandomState.standard_gamma(self, shape, size=None)

Draws samples from a standard Gamma distribution.

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

Parameters

shapefloat: Parameter, must be non-negative.
sizeint or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn.

Returns

outndarray: Drawn samples from the parameterized standard gamma distribution.

Note

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.

Restriction

If shape is neither a scalar nor None : NotImplementedError occurs.

Examples

Draw samples from the distribution:

>>> import nlcpy as vp
>>> shape, scale = 2., 1. # mean and width
>>> s = vp.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.get(), 50, density=True)
>>> y = bins**(shape-1) * ((vp.exp(-bins/scale))/
...                       (sps.gamma(shape) * scale**shape))
>>> plt.plot(bins, y, linewidth=2, color='r') 
>>> plt.show()

../../_images/nlcpy-random-RandomState-standard_gamma-1.png