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# sympy.stats.Laplace

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

The density of the Laplace distribution is given by

.. math::
f(x) := \frac{1}{2 b} \exp \left(-\frac{|x-\mu|}b \right)

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


        def Laplace(name, mu, b):
r"""
Create a continuous random variable with a Laplace distribution.

The density of the Laplace distribution is given by

.. math::
f(x) := \frac{1}{2 b} \exp \left(-\frac{|x-\mu|}b \right)

Parameters
==========

mu : Real number, the location (mean)
b : Real number, b > 0, a scale

Returns
=======

A RandomSymbol.

Examples
========

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

>>> mu = Symbol("mu")
>>> b = Symbol("b", positive=True)
>>> z = Symbol("z")

>>> X = Laplace("x", mu, b)

>>> density(X)(z)
exp(-Abs(-mu + z)/b)/(2*b)

References
==========

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

return rv(name, LaplaceDistribution, (mu, b))


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_laplace():
mu = Symbol("mu")
b = Symbol("b", positive=True)

X = Laplace('x', mu, b)