standard_gamma(shape, size=None, dtype=np.float64, out=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.
- shapefloat or array_like of floats
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 * ksamples are drawn. If size is
None(default), a single value is returned if
shapeis a scalar. Otherwise,
np.array(shape).sizesamples are drawn.
- dtypedtype, optional
Desired dtype of the result, only float64 and float32 are supported. Byteorder must be native. The default value is np.float64.
- 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.
- outndarray or scalar
Drawn samples from the parameterized standard gamma distribution.
probability density function, distribution or cumulative density function, etc.
The probability density for the Gamma distribution is
where is the shape and the scale, and 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.
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html
Wikipedia, “Gamma distribution”, https://en.wikipedia.org/wiki/Gamma_distribution
Draw samples from the distribution:
>>> shape, scale = 2., 1. # mean and width >>> s = np.random.default_rng().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()