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bundles / numpy 2.4.3 / numpy / random / RandomState / power

cython_function_or_method

numpy.random:RandomState.power

Signature

def   power ( a ,  size = None )

Summary

Draws samples in [0, 1] from a power distribution with positive exponent a - 1.

Extended Summary

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), 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.

Returns

out : ndarray or scalar

Drawn samples from the parameterized power distribution.

Raises

: ValueError

If a <= 0.

Notes

The probability density function is

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.

Examples

Draw samples from the distribution: 
a = 5. # shape
samples = 1000
s = np.random.power(a, samples)
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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
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plt.plot(x, normed_y)
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plt.show()
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fig-34c65c3afb03b3ff.png
Compare the power function distribution to the inverse of the Pareto. 
rvs = np.random.power(5, 1000000)
rvsp = np.random.pareto(5, 1000000)
xx = np.linspace(0,1,100)
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plt.figure()
plt.hist(rvs, bins=50, density=True)
plt.title('np.random.power(5)')
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plt.figure()
plt.hist(1./(1.+rvsp), bins=50, density=True)
plt.title('inverse of 1 + np.random.pareto(5)')
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plt.figure()
plt.hist(1./(1.+rvsp), bins=50, density=True)
plt.title('inverse of stats.pareto(5)')
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See also

random.Generator.power

which should be used for new code.

Aliases

  • numpy.random.power
  • numpy.random.RandomState.power