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sympy.stats.Logistic

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

The density of the logistic distribution is given by

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

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


        def Logistic(name, mu, s):
r"""
Create a continuous random variable with a logistic distribution.

The density of the logistic distribution is given by

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

Parameters
==========

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

Returns
=======

A RandomSymbol.

Examples
========

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

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

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

>>> density(X)(z)
exp((mu - z)/s)/(s*(exp((mu - z)/s) + 1)**2)

References
==========

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

return rv(name, LogisticDistribution, (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_logistic():
mu = Symbol("mu", real=True)
s = Symbol("s", positive=True)

X = Logistic('x', mu, s)