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# sympy.stats.FDistribution

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

The density of the F distribution is given by

.. math::
f(x) := \frac{\sqrt{\frac{(d_1 x)^{d_1} d_2^{d_2}}
{(d_1 x + d_2)^{d_1 + d_2}}}}
{x \mathrm{B} \left(\frac{d_1}{2}, \frac{d_2}{2}\right)}

with :math:x > 0.(more...)


        def FDistribution(name, d1, d2):
r"""
Create a continuous random variable with a F distribution.

The density of the F distribution is given by

.. math::
f(x) := \frac{\sqrt{\frac{(d_1 x)^{d_1} d_2^{d_2}}
{(d_1 x + d_2)^{d_1 + d_2}}}}
{x \mathrm{B} \left(\frac{d_1}{2}, \frac{d_2}{2}\right)}

with :math:x > 0.

.. TODO - What do these parameters mean?

Parameters
==========

d1 : d_1 > 0 a parameter
d2 : d_2 > 0 a parameter

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import FDistribution, density
>>> from sympy import Symbol, simplify, pprint

>>> d1 = Symbol("d1", positive=True)
>>> d2 = Symbol("d2", positive=True)
>>> z = Symbol("z")

>>> X = FDistribution("x", d1, d2)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
d2
--    ______________________________
2    /       d1            -d1 - d2       /d1   d2\
d2  *\/  (d1*z)  *(d1*z + d2)         *gamma|-- + --|
\2    2 /
-----------------------------------------------------
/d1\      /d2\
z*gamma|--|*gamma|--|
\2 /      \2 /

References
==========

.. [1] http://en.wikipedia.org/wiki/F-distribution
.. [2] http://mathworld.wolfram.com/F-Distribution.html
"""

return rv(name, FDistributionDistribution, (d1, d2))


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_f_distribution():
d1 = Symbol("d1", positive=True)
d2 = Symbol("d2", positive=True)

X = FDistribution("x", d1, d2)