mars.tensor.random.gamma¶

mars.tensor.random.
gamma
(shape, scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None)[source]¶ Draw samples from a Gamma distribution.
Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale (sometimes designated “theta”), where both parameters are > 0.
 Parameters
shape (float or array_like of floats) – The shape of the gamma distribution. Should be greater than zero.
scale (float or array_like of floats, optional) – The scale of the gamma distribution. Should be greater than zero. Default is equal to 1.
size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifshape
andscale
are both scalars. Otherwise,np.broadcast(shape, scale).size
samples are drawn.chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension
gpu (bool, optional) – Allocate the tensor on GPU if True, False as default
dtype (datatype, optional) – Datatype of the returned tensor.
 Returns
out – Drawn samples from the parameterized gamma distribution.
 Return type
Tensor or scalar
See also
scipy.stats.gamma
probability density function, distribution or cumulative density function, etc.
Notes
The probability density for the Gamma distribution is
\[p(x) = x^{k1}\frac{e^{x/\theta}}{\theta^k\Gamma(k)},\]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.
References
 1
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html
 2
Wikipedia, “Gamma distribution”, http://en.wikipedia.org/wiki/Gamma_distribution
Examples
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2) >>> s = mt.random.gamma(shape, scale, 1000).execute()
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> import numpy as np >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> y = bins**(shape1)*(np.exp(bins/scale) / ... (sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show()