def test_lognormal():
mean = Symbol('mu', real=True)
std = Symbol('sigma', positive=True, real=True)
X = LogNormal('x', mean, std)
# The diofant integrator can't do this too well
# assert E(X) == exp(mean+std**2/2)
# assert variance(X) == (exp(std**2)-1) * exp(2*mean + std**2)
# Right now, only density function and sampling works
# Test sampling: Only e^mean in sample std of 0
for i in range(3):
X = LogNormal('x', i, 0)
assert sample(X) == N(exp(i))
# The diofant integrator can't do this too well
# assert E(X) ==
mu = Symbol('mu', extended_real=True)
sigma = Symbol('sigma', positive=True)
X = LogNormal('x', mu, sigma)
assert density(X)(x) == (sqrt(2)*exp(-(-mu + log(x))**2
/ (2*sigma**2))/(2*x*sqrt(pi)*sigma))
X = LogNormal('x', 0, 1) # Mean 0, standard deviation 1
assert density(X)(x) == sqrt(2)*exp(-log(x)**2/2)/(2*x*sqrt(pi))
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