def test_density():
x = Symbol('x')
l = Symbol('l', positive=True)
rate = Beta(l, 2, 3)
X = Poisson(x, rate)
assert isinstance(pspace(X), ProductPSpace)
assert density(X, Eq(rate, rate.symbol)) == PoissonDistribution(l)
def test_beta():
a, b = symbols('alpha beta', positive=True)
B = Beta('x', a, b)
assert pspace(B).domain.set == Interval(0, 1)
dens = density(B)
x = Symbol('x')
assert dens(x) == x**(a - 1)*(1 - x)**(b - 1) / beta(a, b)
# This is too slow
# assert E(B) == a / (a + b)
# assert variance(B) == (a*b) / ((a+b)**2 * (a+b+1))
# Full symbolic solution is too much, test with numeric version
a, b = Integer(1), Integer(2)
B = Beta('x', a, b)
assert expand_func(E(B)) == a/(a + b)
assert expand_func(variance(B)) == (a*b)/(a + b)**2/(a + b + 1)
def test_prefab_sampling():
N = Normal('X', 0, 1)
L = LogNormal('L', 0, 1)
E = Exponential('Ex', 1)
P = Pareto('P', 1, 3)
W = Weibull('W', 1, 1)
U = Uniform('U', 0, 1)
B = Beta('B', 2, 5)
G = Gamma('G', 1, 3)
variables = [N, L, E, P, W, U, B, G]
niter = 10
for var in variables:
for i in range(niter):
assert sample(var) in var.pspace.domain.set