def test_long_precomputed_cdf():
x = symbols("x", real=True, finite=True)
distribs = [
Arcsin("A", -5, 9),
Dagum("D", 4, 10, 3),
Erlang("E", 14, 5),
Frechet("F", 2, 6, -3),
Gamma("G", 2, 7),
GammaInverse("GI", 3, 5),
Kumaraswamy("K", 6, 8),
Laplace("LA", -5, 4),
Logistic("L", -6, 7),
Nakagami("N", 2, 7),
StudentT("S", 4)
]
for distr in distribs:
for _ in range(5):
assert tn(diff(cdf(distr)(x), x),
density(distr)(x),
x,
a=0,
b=0,
c=1,
d=0)
US = UniformSum("US", 5)
pdf01 = density(US)(x).subs(floor(x), 0).doit() # pdf on (0, 1)
cdf01 = cdf(US, evaluate=False)(x).subs(floor(x),
0).doit() # cdf on (0, 1)
assert tn(diff(cdf01, x), pdf01, x, a=0, b=0, c=1, d=0)
def test_studentt():
nu = Symbol("nu", positive=True)
X = StudentT('x', nu)
assert density(X)(x) == (1 + x**2/nu)**(-nu/2 - 1/2)/(sqrt(nu)*beta(1/2, nu/2))
assert cdf(X)(x) == 1/2 + x*gamma(nu/2 + 1/2)*hyper((1/2, nu/2 + 1/2),
(3/2,), -x**2/nu)/(sqrt(pi)*sqrt(nu)*gamma(nu/2))
def test_studentt():
nu = Symbol("nu", positive=True)
X = StudentT('x', nu)
assert density(X)(x) == (1 + x**2/nu)**(-nu/2 - S.Half)/(sqrt(nu)*beta(S.Half, nu/2))
assert cdf(X)(x) == S.Half + x*gamma(nu/2 + S.Half)*hyper((S.Half, nu/2 + S.Half),
(Rational(3, 2),), -x**2/nu)/(sqrt(pi)*sqrt(nu)*gamma(nu/2))
def test_studentt():
nu = Symbol("nu", positive=True)
X = StudentT('x', nu)
assert density(X) == (Lambda(_x, (_x**2 / nu + 1)**(-nu / 2 - S.Half) *
gamma(nu / 2 + S.Half) /
(sqrt(pi) * sqrt(nu) * gamma(nu / 2))))
def test_sample_scipy():
distribs_scipy = [
Beta("B", 1, 1),
BetaPrime("BP", 1, 1),
Cauchy("C", 1, 1),
Chi("C", 1),
Normal("N", 0, 1),
Gamma("G", 2, 7),
GammaInverse("GI", 1, 1),
GaussianInverse("GUI", 1, 1),
Exponential("E", 2),
LogNormal("LN", 0, 1),
Pareto("P", 1, 1),
StudentT("S", 2),
ChiSquared("CS", 2),
Uniform("U", 0, 1)
]
size = 3
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests for _sample_scipy.')
else:
for X in distribs_scipy:
samps = sample(X, size=size, library='scipy')
samps2 = 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_scipy():
distribs_scipy = [
Beta("B", 1, 1),
BetaPrime("BP", 1, 1),
Cauchy("C", 1, 1),
Chi("C", 1),
Normal("N", 0, 1),
Gamma("G", 2, 7),
GammaInverse("GI", 1, 1),
GaussianInverse("GUI", 1, 1),
Exponential("E", 2),
LogNormal("LN", 0, 1),
Pareto("P", 1, 1),
StudentT("S", 2),
ChiSquared("CS", 2),
Uniform("U", 0, 1)
]
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
g_sample = list(
sample(Gamma("G", 2, 7), size=size, numsamples=numsamples))
assert len(g_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_studentt():
nu = Symbol("nu", positive=True)
X = StudentT('x', nu)
assert density(X)(x) == (1 + x**2/nu)**(-nu/2 - 1/2)/(sqrt(nu)*beta(1/2, nu/2))
