nlcpy.random.Generator.standard_gamma

Generator.standard_gamma(self, shape, size=None, dtype='d', out=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.
dtypestr or dtype, optional: Desired dtype of the result, either ‘d’ (or ‘float64’) or ‘f’ (or ‘float32’). All dtypes are determined by their name. The default value is ‘d’.
outndarray, optional: Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values.

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.

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.

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.default_rng().standard_gamma(shape, 1000000)
>>> 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-Generator-standard_gamma-1.png