def test_MarginalDistribution():
a1, p1, p2 = symbols('a1 p1 p2', positive=True)
C = Multinomial('C', 2, p1, p2)
B = MultivariateBeta('B', a1, C[0])
MGR = MarginalDistribution(B, (C[0], ))
mgrc = Mul(
Symbol('B'),
Piecewise(
ExprCondPair(
Mul(
Integer(2),
Pow(Symbol('p1', positive=True),
Indexed(IndexedBase(Symbol('C')), Integer(0))),
Pow(Symbol('p2', positive=True),
Indexed(IndexedBase(Symbol('C')), Integer(1))),
Pow(
factorial(Indexed(IndexedBase(Symbol('C')),
Integer(0))), Integer(-1)),
Pow(
factorial(Indexed(IndexedBase(Symbol('C')),
Integer(1))), Integer(-1))),
Eq(
Add(Indexed(IndexedBase(Symbol('C')), Integer(0)),
Indexed(IndexedBase(Symbol('C')), Integer(1))),
Integer(2))), ExprCondPair(Integer(0), True)),
Pow(gamma(Symbol('a1', positive=True)), Integer(-1)),
gamma(
Add(Symbol('a1', positive=True),
Indexed(IndexedBase(Symbol('C')), Integer(0)))),
Pow(gamma(Indexed(IndexedBase(Symbol('C')), Integer(0))), Integer(-1)),
Pow(Indexed(IndexedBase(Symbol('B')), Integer(0)),
Add(Symbol('a1', positive=True), Integer(-1))),
Pow(Indexed(IndexedBase(Symbol('B')), Integer(1)),
Add(Indexed(IndexedBase(Symbol('C')), Integer(0)), Integer(-1))))
assert MGR(C) == mgrc
def JointRV(symbol, pdf, _set=None):
"""
Create a Joint Random Variable where each of its component is continuous,
given the following:
Parameters
==========
symbol : Symbol
Represents name of the random variable.
pdf : A PDF in terms of indexed symbols of the symbol given
as the first argument
NOTE
====
As of now, the set for each component for a ``JointRV`` is
equal to the set of all integers, which cannot be changed.
Examples
========
>>> from sympy import exp, pi, Indexed, S
>>> from sympy.stats import density, JointRV
>>> x1, x2 = (Indexed('x', i) for i in (1, 2))
>>> pdf = exp(-x1**2/2 + x1 - x2**2/2 - S(1)/2)/(2*pi)
>>> N1 = JointRV('x', pdf) #Multivariate Normal distribution
>>> density(N1)(1, 2)
exp(-2)/(2*pi)
Returns
=======
RandomSymbol
"""
#TODO: Add support for sets provided by the user
symbol = sympify(symbol)
syms = list(i for i in pdf.free_symbols if isinstance(i, Indexed)
and i.base == IndexedBase(symbol))
syms = tuple(sorted(syms, key = lambda index: index.args[1]))
_set = S.Reals**len(syms)
pdf = Lambda(syms, pdf)
dist = JointDistributionHandmade(pdf, _set)
jrv = JointPSpace(symbol, dist).value
rvs = random_symbols(pdf)
if len(rvs) != 0:
dist = MarginalDistribution(dist, (jrv,))
return JointPSpace(symbol, dist).value
return jrv
