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# sympy.stats.Frechet

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

The density of the Frechet distribution is given by

.. math::
f(x) := \frac{\alpha}{s} \left(\frac{x-m}{s}\right)^{-1-\alpha}
e^{-(\frac{x-m}{s})^{-\alpha}}

with :math:x \geq m.
(more...)


        def Frechet(name, a, s=1, m=0):
r"""
Create a continuous random variable with a Frechet distribution.

The density of the Frechet distribution is given by

.. math::
f(x) := \frac{\alpha}{s} \left(\frac{x-m}{s}\right)^{-1-\alpha}
e^{-(\frac{x-m}{s})^{-\alpha}}

with :math:x \geq m.

Parameters
==========

a : Real number, :math:a \in \left(0, \infty\right) the shape
s : Real number, :math:s \in \left(0, \infty\right) the scale
m : Real number, :math:m \in \left(-\infty, \infty\right) the minimum

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import Frechet, density, E, std
>>> from sympy import Symbol, simplify

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

>>> X = Frechet("x", a, s, m)

>>> density(X)(z)
a*((-m + z)/s)**(-a - 1)*exp(-((-m + z)/s)**(-a))/s

References
==========

.. [1] http://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution
"""

return rv(name, FrechetDistribution, (a, s, m))


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,

    m = Symbol("m", real=True)

X = Frechet("x", a, s=s, m=m)
assert density(X)(x) == a*((x - m)/s)**(-a - 1)*exp(-((x - m)/s)**(-a))/s