def test_moment_generating_functions():
t = S('t')
geometric_mgf = moment_generating_function(Geometric('g', S.Half))(t)
assert geometric_mgf.diff(t).subs(t, 0) == 2
logarithmic_mgf = moment_generating_function(Logarithmic('l', S.Half))(t)
assert logarithmic_mgf.diff(t).subs(t, 0) == 1 / log(2)
negative_binomial_mgf = moment_generating_function(
NegativeBinomial('n', 5, Rational(1, 3)))(t)
assert negative_binomial_mgf.diff(t).subs(t, 0) == Rational(5, 2)
poisson_mgf = moment_generating_function(Poisson('p', 5))(t)
assert poisson_mgf.diff(t).subs(t, 0) == 5
skellam_mgf = moment_generating_function(Skellam('s', 1, 1))(t)
assert skellam_mgf.diff(t).subs(
t, 2) == (-exp(-2) + exp(2)) * exp(-2 + exp(-2) + exp(2))
yule_simon_mgf = moment_generating_function(YuleSimon('y', 3))(t)
assert simplify(yule_simon_mgf.diff(t).subs(t, 0)) == Rational(3, 2)
zeta_mgf = moment_generating_function(Zeta('z', 5))(t)
assert zeta_mgf.diff(t).subs(t, 0) == pi**4 / (90 * zeta(5))
def test_sample_scipy():
p = S(2) / 3
x = Symbol('x', integer=True, positive=True)
pdf = p * (1 - p)**(x - 1) # pdf of Geometric Distribution
distribs_scipy = [
DiscreteRV(x, pdf, set=S.Naturals),
Geometric('G', 0.5),
Logarithmic('L', 0.5),
NegativeBinomial('N', 5, 0.4),
Poisson('P', 1),
Skellam('S', 1, 1),
YuleSimon('Y', 1),
Zeta('Z', 2)
]
size = 3
numsamples = 5
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests for _sample_scipy.')
else:
with ignore_warnings(
UserWarning
): ### TODO: Restore tests once warnings are removed
z_sample = list(
sample(Zeta("G", 7), size=size, numsamples=numsamples))
assert len(z_sample) == numsamples
for X in distribs_scipy:
samps = next(sample(X, size=size, library='scipy'))
samps2 = next(sample(X, size=(2, 2), library='scipy'))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
def test_sample_numpy():
distribs_numpy = [Geometric('G', 0.5), Poisson('P', 1), Zeta('Z', 2)]
size = 3
numpy = import_module('numpy')
if not numpy:
skip('Numpy is not installed. Abort tests for _sample_numpy.')
else:
with ignore_warnings(UserWarning):
for X in distribs_numpy:
samps = next(sample(X, size=size, library='numpy'))
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError,
lambda: next(sample(Skellam('S', 1, 1), library='numpy')))
raises(
NotImplementedError, lambda: Skellam('S', 1, 1).pspace.distribution.
sample(library='tensorflow'))
def test_skellam():
mu1 = Symbol('mu1')
mu2 = Symbol('mu2')
z = Symbol('z')
X = Skellam('x', mu1, mu2)
assert density(X)(z) == (mu1/mu2)**(z/2) * \
exp(-mu1 - mu2)*besseli(z, 2*sqrt(mu1*mu2))
assert skewness(X).expand() == mu1/(mu1*sqrt(mu1 + mu2) + mu2 *
sqrt(mu1 + mu2)) - mu2/(mu1*sqrt(mu1 + mu2) + mu2*sqrt(mu1 + mu2))
assert variance(X).expand() == mu1 + mu2
assert E(X) == mu1 - mu2
assert characteristic_function(X)(z) == exp(
mu1*exp(I*z) - mu1 - mu2 + mu2*exp(-I*z))
assert moment_generating_function(X)(z) == exp(
mu1*exp(z) - mu1 - mu2 + mu2*exp(-z))
def test_sampling_methods():
distribs_numpy = [
Geometric('G', 0.5),
Poisson('P', 1),
Zeta('Z', 2)
]
distribs_scipy = [
Geometric('G', 0.5),
Logarithmic('L', 0.5),
Poisson('P', 1),
Skellam('S', 1, 1),
YuleSimon('Y', 1),
Zeta('Z', 2)
]
distribs_pymc3 = [
Geometric('G', 0.5),
Poisson('P', 1),
]
size = 3
numpy = import_module('numpy')
if not numpy:
skip('Numpy is not installed. Abort tests for _sample_numpy.')
else:
with ignore_warnings(UserWarning):
for X in distribs_numpy:
samps = X.pspace.distribution._sample_numpy(size)
for samp in samps:
assert samp in X.pspace.domain.set
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests for _sample_scipy.')
else:
with ignore_warnings(UserWarning):
for X in distribs_scipy:
samps = next(sample(X, size=size))
for samp in samps:
assert samp in X.pspace.domain.set
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
with ignore_warnings(UserWarning):
for X in distribs_pymc3:
samps = X.pspace.distribution._sample_pymc3(size)
for samp in samps:
assert samp in X.pspace.domain.set
def test_sample_pymc3():
distribs_pymc3 = [
Geometric('G', 0.5),
Poisson('P', 1),
NegativeBinomial('N', 5, 0.4)
]
size = 3
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
with ignore_warnings(UserWarning): ### TODO: Restore tests once warnings are removed
for X in distribs_pymc3:
samps = next(sample(X, size=size, library='pymc3'))
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError,
lambda: next(sample(Skellam('S', 1, 1), library='pymc3')))
