def test_Multinomial():
from sympy.stats.joint_rv_types import Multinomial
n, x1, x2, x3, x4 = symbols('n, x1, x2, x3, x4', nonnegative=True, integer=True)
p1, p2, p3, p4 = symbols('p1, p2, p3, p4', positive=True)
p1_f = symbols('p1_f', negative=True)
M = Multinomial('M', 3, [p1, p2, p3, p4])
M_c = Multinomial('C', 3, 0.5, 0.4, 0.3, 0.2)
f = factorial
assert simplify(density(M)(x1, x2, x3, x4) -
S(6)*p1**x1*p2**x2*p3**x3*p4**x4/(f(x1)*f(x2)*f(x3)*f(x4))) == S(0)
assert marginal_distribution(M_c, M_c[0])(1).round(2) == 7.29
raises(ValueError, lambda: Multinomial('b1', 5, [p1, p2, p3, p1_f]))
raises(ValueError, lambda: Multinomial('b2', n, [p1, p2, p3, p4]))
def test_Multinomial():
n, x1, x2, x3, x4 = symbols('n, x1, x2, x3, x4', nonnegative=True, integer=True)
p1, p2, p3, p4 = symbols('p1, p2, p3, p4', positive=True)
p1_f, n_f = symbols('p1_f, n_f', negative=True)
M = Multinomial('M', n, [p1, p2, p3, p4])
C = Multinomial('C', 3, p1, p2, p3)
f = factorial
assert density(M)(x1, x2, x3, x4) == Piecewise((p1**x1*p2**x2*p3**x3*p4**x4*
f(n)/(f(x1)*f(x2)*f(x3)*f(x4)),
Eq(n, x1 + x2 + x3 + x4)), (0, True))
assert marginal_distribution(C, C[0])(x1).subs(x1, 1) ==\
3*p1*p2**2 +\
6*p1*p2*p3 +\
3*p1*p3**2
raises(ValueError, lambda: Multinomial('b1', 5, [p1, p2, p3, p1_f]))
raises(ValueError, lambda: Multinomial('b2', n_f, [p1, p2, p3, p4]))
raises(ValueError, lambda: Multinomial('b3', n, 0.5, 0.4, 0.3, 0.1))
def test_Multinomial():
from sympy.stats.joint_rv_types import Multinomial
n, x1, x2, x3, x4 = symbols("n, x1, x2, x3, x4",
nonnegative=True,
integer=True)
p1, p2, p3, p4 = symbols("p1, p2, p3, p4", positive=True)
p1_f, n_f = symbols("p1_f, n_f", negative=True)
M = Multinomial("M", n, [p1, p2, p3, p4])
C = Multinomial("C", 3, p1, p2, p3)
f = factorial
assert density(M)(x1, x2, x3, x4) == Piecewise(
(
p1**x1 * p2**x2 * p3**x3 * p4**x4 * f(n) /
(f(x1) * f(x2) * f(x3) * f(x4)),
Eq(n, x1 + x2 + x3 + x4),
),
(0, True),
)
assert (marginal_distribution(C, C[0])(x1).subs(x1, 1) == 3 * p1 * p2**2 +
6 * p1 * p2 * p3 + 3 * p1 * p3**2)
raises(ValueError, lambda: Multinomial("b1", 5, [p1, p2, p3, p1_f]))
raises(ValueError, lambda: Multinomial("b2", n_f, [p1, p2, p3, p4]))
raises(ValueError, lambda: Multinomial("b3", n, 0.5, 0.4, 0.3, 0.1))
def test_sample_pymc3():
distribs_pymc3 = [
MultivariateNormal("M", [5, 2], [[1, 0], [0, 1]]),
MultivariateBeta("B", [0.4, 5, 15]),
Multinomial("N", 4, [0.3, 0.2, 0.1, 0.4])
]
size = 3
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
for X in distribs_pymc3:
samps = sample(X, size=size, library='pymc3')
for sam in samps:
assert tuple(sam.flatten()) in X.pspace.distribution.set
N_c = NegativeMultinomial('N', 3, 0.1, 0.1, 0.1)
raises(NotImplementedError, lambda: sample(N_c, library='pymc3'))
def test_sample_numpy():
distribs_numpy = [
MultivariateNormal("M", [3, 4], [[2, 1], [1, 2]]),
MultivariateBeta("B", [0.4, 5, 15, 50, 203]),
Multinomial("N", 50, [0.3, 0.2, 0.1, 0.25, 0.15])
]
size = 3
numpy = import_module('numpy')
if not numpy:
skip('Numpy is not installed. Abort tests for _sample_numpy.')
else:
for X in distribs_numpy:
samps = sample(X, size=size, library='numpy')
for sam in samps:
assert tuple(sam) in X.pspace.distribution.set
N_c = NegativeMultinomial('N', 3, 0.1, 0.1, 0.1)
raises(NotImplementedError, lambda: sample(N_c, library='numpy'))
def test_sample_scipy():
distribs_scipy = [
MultivariateNormal("M", [0, 0], [[0.1, 0.025], [0.025, 0.1]]),
MultivariateBeta("B", [0.4, 5, 15]),
Multinomial("N", 8, [0.3, 0.2, 0.1, 0.4])
]
size = 3
scipy = import_module('scipy')
if not scipy:
skip('Scipy not installed. Abort tests for _sample_scipy.')
else:
for X in distribs_scipy:
samps = sample(X, size=size)
samps2 = sample(X, size=(2, 2))
for sam in samps:
assert tuple(sam) in X.pspace.distribution.set
for i in range(2):
for j in range(2):
assert tuple(samps2[i][j]) in X.pspace.distribution.set
N_c = NegativeMultinomial('N', 3, 0.1, 0.1, 0.1)
raises(NotImplementedError, lambda: sample(N_c))