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# sympy.stats.RaisedCosine

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a Continuous Random Variable with a raised cosine distribution.

The density of the raised cosine distribution is given by

.. math::
f(x) := \frac{1}{2s}\left(1+\cos\left(\frac{x-\mu}{s}\pi\right)\right)

with :math:x \in [\mu-s,\mu+s].

Parameters(more...)


        def RaisedCosine(name, mu, s):
r"""
Create a Continuous Random Variable with a raised cosine distribution.

The density of the raised cosine distribution is given by

.. math::
f(x) := \frac{1}{2s}\left(1+\cos\left(\frac{x-\mu}{s}\pi\right)\right)

with :math:x \in [\mu-s,\mu+s].

Parameters
==========

mu : Real number
s : Real number, s > 0

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import RaisedCosine, density, E, variance
>>> from sympy import Symbol, simplify, pprint

>>> mu = Symbol("mu", real=True)
>>> s = Symbol("s", positive=True)
>>> z = Symbol("z")

>>> X = RaisedCosine("x", mu, s)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
/   /pi*(-mu + z)\
|cos|------------| + 1
|   \     s      /
<---------------------  for And(z <= mu + s, mu - s <= z)
|         2*s
|
\          0                        otherwise

References
==========

.. [1] http://en.wikipedia.org/wiki/Raised_cosine_distribution
"""

return rv(name, RaisedCosineDistribution, (mu, s))


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_raised_cosine():
mu = Symbol("mu", real=True)
s = Symbol("s", positive=True)

X = RaisedCosine("x", mu, s)