standard_cauchy(self, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.standard_cauchy.
Some inconsistencies with the Dask version may exist.
Also known as the Lorentz distribution.
New code should use the standard_cauchy
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability density function for the full Cauchy distribution is
$$P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+(\frac{x-x_0}{\gamma})^2 \bigr] }$$and the Standard Cauchy distribution just sets $x_0=0$ and $\gamma=1$
The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis.
When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails.
Output shape. If the given shape is, e.g., (m, n, k)
, then m * n * k
samples are drawn. Default is None, in which case a single value is returned.
The drawn samples.
Draw samples from a standard Cauchy distribution with mode = 0.
Generator.standard_cauchy
which should be used for new code.
Draw samples and plot the distribution:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIPSee :
... s = np.random.standard_cauchy(1000000) # doctest: +SKIP
... s = s[(s>-25) & (s<25)] # truncate distribution so it plots well # doctest: +SKIP
... plt.hist(s, bins=100) # doctest: +SKIP
... plt.show() # doctest: +SKIP
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