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