power

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power#

class brainstate.random.power(a, size=None, key=None, dtype=None)#

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. Must be non-negative.

  • size (int | Sequence[int] | integer | Sequence[integer] | None) – 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 a is a scalar. Otherwise, np.array(a).size samples are drawn.

  • key (int | Array | ndarray | None) – The key for the random number generator. If not given, the default random number generator is used.

Returns:

out – Drawn samples from the parameterized power distribution.

Return type:

ndarray or scalar

Raises:

ValueError – If a <= 0.

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

Examples

Draw samples from the distribution:

>>> import brainstate
>>> a = 5. # shape
>>> samples = 1000
>>> s = brainstate.random.power(a, samples)

Display the histogram of the samples, along with the probability density function:

>>> import matplotlib.pyplot as plt  # noqa
>>> count, bins, ignored = plt.hist(s, bins=30)
>>> x = np.linspace(0, 1, 100)
>>> y = a*x**(a-1.)
>>> normed_y = samples*np.diff(bins)[0]*y
>>> plt.plot(x, normed_y)
>>> plt.show()

Compare the power function distribution to the inverse of the Pareto.

>>> from scipy import stats
>>> rvs = brainstate.random.power(5, 1000000)
>>> rvsp = brainstate.random.pareto(5, 1000000)
>>> xx = np.linspace(0,1,100)
>>> powpdf = stats.powerlaw.pdf(xx,5)

>>> plt.figure()
>>> plt.hist(rvs, bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('brainstate.random.power(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('inverse of 1 + brainstate.random.pareto(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('inverse of stats.pareto(5)')
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