brainpy.math.random.power#
- brainpy.math.random.power(a, size=None, key=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. Must be non-negative.
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,np.array(a).size
samples are drawn.
- 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:
>>> a = 5. # shape >>> samples = 1000 >>> s = bm.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, 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 = bm.random.power(5, 1000000) >>> rvsp = bm.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('bm.random.power(5)')
>>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') >>> plt.title('inverse of 1 + bm.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)')