power(self, a, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.power.
Some inconsistencies with the Dask version may exist.
Also known as the power function distribution.
New code should use the power
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
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.
Parameter of the distribution. Must be non-negative.
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.
If a <= 0.
Drawn samples from the parameterized power distribution.
Draws samples in [0, 1] from a power distribution with positive exponent a - 1.
Generator.power
which should be used for new code.
Draw samples from the distribution:
This example is valid syntax, but we were not able to check execution>>> a = 5. # shape # doctest: +SKIP
... samples = 1000 # doctest: +SKIP
... s = np.random.power(a, samples) # doctest: +SKIP
Display the histogram of the samples, along with the probability density function:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIP
... count, bins, ignored = plt.hist(s, bins=30) # doctest: +SKIP
... x = np.linspace(0, 1, 100) # doctest: +SKIP
... y = a*x**(a-1.) # doctest: +SKIP
... normed_y = samples*np.diff(bins)[0]*y # doctest: +SKIP
... plt.plot(x, normed_y) # doctest: +SKIP
... plt.show() # doctest: +SKIP
Compare the power function distribution to the inverse of the Pareto.
This example is valid syntax, but we were not able to check execution>>> from scipy import stats # doctest: +SKIPThis example is valid syntax, but we were not able to check execution
... rvs = np.random.power(5, 1000000) # doctest: +SKIP
... rvsp = np.random.pareto(5, 1000000) # doctest: +SKIP
... xx = np.linspace(0,1,100) # doctest: +SKIP
... powpdf = stats.powerlaw.pdf(xx,5) # doctest: +SKIP
>>> plt.figure() # doctest: +SKIPThis example is valid syntax, but we were not able to check execution
... plt.hist(rvs, bins=50, density=True) # doctest: +SKIP
... plt.plot(xx,powpdf,'r-') # doctest: +SKIP
... plt.title('np.random.power(5)') # doctest: +SKIP
>>> plt.figure() # doctest: +SKIPThis example is valid syntax, but we were not able to check execution
... plt.hist(1./(1.+rvsp), bins=50, density=True) # doctest: +SKIP
... plt.plot(xx,powpdf,'r-') # doctest: +SKIP
... plt.title('inverse of 1 + np.random.pareto(5)') # doctest: +SKIP
>>> plt.figure() # doctest: +SKIPSee :
... plt.hist(1./(1.+rvsp), bins=50, density=True) # doctest: +SKIP
... plt.plot(xx,powpdf,'r-') # doctest: +SKIP
... plt.title('inverse of stats.pareto(5)') # doctest: +SKIP
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