flopscope.

flopscope.numpy.random.RandomState.standard_gamma

fnp.random.RandomState.standard_gamma(self, shape, size=None)

Draw samples from a standard Gamma distribution.

Adapted from NumPy docs np.random.RandomState.standard_gamma

Arearandom
Typecounted
NumPy Refnp.random.RandomState.standard_gamma
Cost
numel(output)\text{numel}(\text{output})
Flopscope Context

Legacy standard gamma; cost = numel(output).

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

Note.

New code should use the standard_gamma method of a Generator instance instead; please see the random-quick-start.

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, flops.array(shape).size samples are drawn.

Returns

out:ndarray or scalar

Drawn samples from the parameterized standard gamma distribution.

See also

Notes

The probability density for the Gamma distribution is

p(x)=xk−1e−x/θθkΓ(k),p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},

where kk is the shape and θ\theta the scale, and Γ\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

footnote
1

Weisstein, Eric W. "Gamma Distribution." From MathWorld--A
Wolfram Web Resource.
https://mathworld.wolfram.com/GammaDistribution.html
footnote
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 = flops.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  # doctest: +SKIP
>>> count, bins, ignored = plt.hist(s, 50, density=True)
>>> y = bins**(shape-1) * ((flops.exp(-bins/scale))/  # doctest: +SKIP
... (sps.gamma(shape) * scale**shape))
>>> plt.plot(bins, y, linewidth=2, color='r')  # doctest: +SKIP
>>> plt.show()