def test_MultivariateTDist():
t1 = MultivariateT('T', [0, 0], [[1, 0], [0, 1]], 2)
assert(density(t1))(1, 1) == 1/(8*pi)
assert t1.pspace.distribution.set == ProductSet(S.Reals, S.Reals)
assert integrate(density(t1)(x, y), (x, -oo, oo), \
(y, -oo, oo)).evalf() == 1
raises(ValueError, lambda: MultivariateT('T', [1, 2], [[1, 1], [1, -1]], 1))
t2 = MultivariateT('t2', [1, 2], [[x, 0], [0, y]], 1)
assert density(t2)(1, 2) == 1/(2*pi*sqrt(x*y))
def test_MultivariateTDist():
from sympy.stats.joint_rv_types import MultivariateT
t1 = MultivariateT('T', [0, 0], [[1, 0], [0, 1]], 2)
assert(density(t1))(1, 1) == 1/(8*pi)
assert integrate(density(t1)(x, y), (x, -oo, oo), \
(y, -oo, oo)).evalf() == 1
raises(ValueError, lambda: MultivariateT('T', [1, 2], [[1, 1], [1, -1]], 1))
t2 = MultivariateT('t2', [1, 2], [[x, 0], [0, y]], 1)
assert density(t2)(1, 2) == 1/(2*pi*sqrt(x*y))
def test_JointPSpace_marginal_distribution():
T = MultivariateT('T', [0, 0], [[1, 0], [0, 1]], 2)
got = marginal_distribution(T, T[1])(x)
ans = sqrt(2)*(x**2/2 + 1)/(4*polar_lift(x**2/2 + 1)**(S(5)/2))
assert got == ans, got
assert integrate(marginal_distribution(T, 1)(x), (x, -oo, oo)) == 1
t = MultivariateT('T', [0, 0, 0], [[1, 0, 0], [0, 1, 0], [0, 0, 1]], 3)
assert comp(marginal_distribution(t, 0)(1).evalf(), 0.2, .01)
def test_JointPSpace_marginal_distribution():
from sympy.stats.joint_rv_types import MultivariateT
from sympy import polar_lift
T = MultivariateT('T', [0, 0], [[1, 0], [0, 1]], 2)
assert marginal_distribution(T, T[1])(x) == sqrt(2)*(x**2 + 2)/(
8*polar_lift(x**2/2 + 1)**Rational(5, 2))
assert integrate(marginal_distribution(T, 1)(x), (x, -oo, oo)) == 1
t = MultivariateT('T', [0, 0, 0], [[1, 0, 0], [0, 1, 0], [0, 0, 1]], 3)
assert comp(marginal_distribution(t, 0)(1).evalf(), 0.2, .01)
def test_JointPSpace_margial_distribution():
from sympy.stats.joint_rv_types import MultivariateT
from sympy import polar_lift
T = MultivariateT('T', [0, 0], [[1, 0], [0, 1]], 2)
assert marginal_distribution(
T, T[1])(x) == sqrt(2) * (x**2 +
2) / (8 * polar_lift(x**2 / 2 + 1)**(5 / 2))
assert integrate(marginal_distribution(T, 1)(x), (x, -oo, oo)) == 1
