mars.tensor.random.power#
- mars.tensor.random.power(a, size=None, chunk_size=None, gpu=None, dtype=None)[source]#
Draws samples in [0, 1] from a power distribution with positive exponent a - 1.
Also known as the power function distribution.
- Parameters
a (float or array_like of floats) – Parameter of the distribution. Should be greater than zero.
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 ifa
is a scalar. Otherwise,mt.array(a).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 (data-type, optional) – Data-type of the returned tensor.
- Returns
out – Drawn samples from the parameterized power distribution.
- Return type
Tensor or scalar
- Raises
ValueError – If a < 1.
Notes
The probability density function is
\[P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0.\]The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution.
It is used, for example, in modeling the over-reporting of insurance claims.
References
- 1
Christian Kleiber, Samuel Kotz, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.
- 2
Heckert, N. A. and Filliben, James J. “NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions”, National Institute of Standards and Technology Handbook Series, June 2003. http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf
Examples
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> a = 5. # shape >>> samples = 1000 >>> s = mt.random.power(a, samples)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s.execute(), bins=30) >>> x = mt.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*mt.diff(bins)[0]*y >>> plt.plot(x.execute(), normed_y.execute()) >>> plt.show()
Compare the power function distribution to the inverse of the Pareto.
>>> from scipy import stats >>> rvs = mt.random.power(5, 1000000) >>> rvsp = mt.random.pareto(5, 1000000) >>> xx = mt.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx.execute(),5)
>>> plt.figure() >>> plt.hist(rvs.execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('np.random.power(5)')
>>> plt.figure() >>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('inverse of 1 + np.random.pareto(5)')
>>> plt.figure() >>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True) >>> plt.plot(xx.execute(),powpdf,'r-') >>> plt.title('inverse of stats.pareto(5)')