def test_MultivariateEwens():
n, theta, i = symbols('n theta i', positive=True)
# tests for integer dimensions
theta_f = symbols('t_f', negative=True)
a = symbols('a_1:4', positive=True, integer=True)
ed = MultivariateEwens('E', 3, theta)
assert density(ed)(a[0], a[1], a[2]) == Piecewise(
(6 * 2**(-a[1]) * 3**(-a[2]) * theta**a[0] * theta**a[1] *
theta**a[2] /
(theta * (theta + 1) *
(theta + 2) * factorial(a[0]) * factorial(a[1]) * factorial(a[2])),
Eq(a[0] + 2 * a[1] + 3 * a[2], 3)), (0, True))
assert marginal_distribution(ed, ed[1])(a[1]) == Piecewise(
(6 * 2**(-a[1]) * theta**a[1] /
((theta + 1) * (theta + 2) * factorial(a[1])), Eq(2 * a[1] + 1, 3)),
(0, True))
raises(ValueError, lambda: MultivariateEwens('e1', 5, theta_f))
assert ed.pspace.distribution.set == ProductSet(Range(0, 4, 1),
Range(0, 2, 1),
Range(0, 2, 1))
# tests for symbolic dimensions
eds = MultivariateEwens('E', n, theta)
a = IndexedBase('a')
j, k = symbols('j, k')
den = Piecewise((factorial(n) *
Product(theta**a[j] * (j + 1)**(-a[j]) / factorial(a[j]),
(j, 0, n - 1)) / RisingFactorial(theta, n),
Eq(n, Sum((k + 1) * a[k], (k, 0, n - 1)))), (0, True))
assert density(eds)(a).dummy_eq(den)
def test_MultivariateEwens():
from sympy.stats.joint_rv_types import MultivariateEwens
n, theta = symbols('n theta', positive=True)
theta_f = symbols('t_f', negative=True)
a = symbols('a_1:4', positive = True, integer = True)
ed = MultivariateEwens('E', 3, theta)
assert density(ed)(a[0], a[1], a[2]) == Piecewise((6*2**(-a[1])*3**(-a[2])*
theta**a[0]*theta**a[1]*theta**a[2]/
(theta*(theta + 1)*(theta + 2)*
factorial(a[0])*factorial(a[1])*
factorial(a[2])), Eq(a[0] + 2*a[1] +
3*a[2], 3)), (0, True))
assert marginal_distribution(ed, ed[1])(a[1]) == Piecewise((6*2**(-a[1])*
theta**a[1]/((theta + 1)*
(theta + 2)*factorial(a[1])),
Eq(2*a[1] + 1, 3)), (0, True))
raises(ValueError, lambda: MultivariateEwens('e1', 5, theta_f))
raises(ValueError, lambda: MultivariateEwens('e1', n, theta))
def test_MultivariateEwens():
from sympy.stats.joint_rv_types import MultivariateEwens
n, theta, i = symbols("n theta i", positive=True)
# tests for integer dimensions
theta_f = symbols("t_f", negative=True)
a = symbols("a_1:4", positive=True, integer=True)
ed = MultivariateEwens("E", 3, theta)
assert density(ed)(a[0], a[1], a[2]) == Piecewise(
(
6 * 2**(-a[1]) * 3**(-a[2]) * theta**a[0] * theta**a[1] *
theta**a[2] / (theta * (theta + 1) *
(theta + 2) * factorial(a[0]) * factorial(a[1]) *
factorial(a[2])),
Eq(a[0] + 2 * a[1] + 3 * a[2], 3),
),
(0, True),
)
assert marginal_distribution(ed, ed[1])(a[1]) == Piecewise(
(
6 * 2**(-a[1]) * theta**a[1] / ((theta + 1) *
(theta + 2) * factorial(a[1])),
Eq(2 * a[1] + 1, 3),
),
(0, True),
)
raises(ValueError, lambda: MultivariateEwens("e1", 5, theta_f))
# tests for symbolic dimensions
eds = MultivariateEwens("E", n, theta)
a = IndexedBase("a")
j, k = symbols("j, k")
den = Piecewise(
(
factorial(n) *
Product(theta**a[j] * (j + 1)**(-a[j]) / factorial(a[j]),
(j, 0, n - 1)) / RisingFactorial(theta, n),
Eq(n, Sum((k + 1) * a[k], (k, 0, n - 1))),
),
(0, True),
)
assert density(eds)(a).dummy_eq(den)