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# sympy.stats.Beta

All Samples(6)  |  Call(4)  |  Derive(0)  |  Import(2)
Create a Continuous Random Variable with a Beta distribution.

The density of the Beta distribution is given by

.. math::
f(x) := \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}

with :math:x \in [0,1].

Parameters(more...)


        def Beta(name, alpha, beta):
r"""
Create a Continuous Random Variable with a Beta distribution.

The density of the Beta distribution is given by

.. math::
f(x) := \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}

with :math:x \in [0,1].

Parameters
==========

alpha : Real number, \alpha > 0, a shape
beta : Real number, \beta > 0, a shape

Returns
=======

A RandomSymbol.

Examples
========

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

>>> alpha = Symbol("alpha", positive=True)
>>> beta = Symbol("beta", positive=True)
>>> z = Symbol("z")

>>> X = Beta("x", alpha, beta)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
alpha - 1         beta - 1
z         *(-z + 1)        *gamma(alpha + beta)
-----------------------------------------------
gamma(alpha)*gamma(beta)

>>> simplify(E(X, meijerg=True))
alpha/(alpha + beta)

>>> simplify(variance(X, meijerg=True))  #doctest: +SKIP
alpha*beta/((alpha + beta)**2*(alpha + beta + 1))

References
==========

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



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_beta():
a, b = symbols('alpha beta', positive=True)

B = Beta('x', a, b)

assert pspace(B).domain.set == Interval(0, 1)

dens = density(B)

    # Full symbolic solution is too much, test with numeric version
a, b = 1, 2
B = Beta('x', a, b)
assert E(B) == a / S(a + b)
assert variance(B) == (a*b) / S((a + b)**2 * (a + b + 1))


from sympy.stats import Poisson, Beta