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# sympy.stats.Cauchy

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a continuous random variable with a Cauchy distribution.

The density of the Cauchy distribution is given by

.. math::
f(x) := \frac{1}{\pi} \arctan\left(\frac{x-x_0}{\gamma}\right)
+\frac{1}{2}

Parameters
==========(more...)


        def Cauchy(name, x0, gamma):
r"""
Create a continuous random variable with a Cauchy distribution.

The density of the Cauchy distribution is given by

.. math::
f(x) := \frac{1}{\pi} \arctan\left(\frac{x-x_0}{\gamma}\right)
+\frac{1}{2}

Parameters
==========

x0 : Real number, the location
gamma : Real number, \gamma > 0, the scale

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import Cauchy, density
>>> from sympy import Symbol

>>> x0 = Symbol("x0")
>>> gamma = Symbol("gamma", positive=True)
>>> z = Symbol("z")

>>> X = Cauchy("x", x0, gamma)

>>> density(X)(z)
1/(pi*gamma*(1 + (-x0 + z)**2/gamma**2))

References
==========

.. [1] http://en.wikipedia.org/wiki/Cauchy_distribution
.. [2] http://mathworld.wolfram.com/CauchyDistribution.html
"""

return rv(name, CauchyDistribution, (x0, gamma))


from sympy.stats import (P, E, where, density, variance, covariance, skewness,
given, pspace, cdf, ContinuousRV, sample,
Arcsin, Benini, Beta, BetaPrime, Cauchy,
Chi, ChiSquared,
ChiNoncentral, Dagum, Erlang, Exponential,

def test_cauchy():
x0 = Symbol("x0")
gamma = Symbol("gamma", positive=True)

X = Cauchy('x', x0, gamma)