def test_1D_is_invgamma(self):
# The 1-dimensional inverse Wishart with an identity scale matrix is
# just an inverse gamma distribution.
# Test variance, mean, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(5, 20, 2, dtype=float)
X = np.linspace(0.1,10,num=10)
for df in df_range:
iw = invwishart(df, scale)
ig = invgamma(df/2, scale=1./2)
# Statistics
assert_allclose(iw.var(), ig.var())
assert_allclose(iw.mean(), ig.mean())
# PDF
assert_allclose(iw.pdf(X), ig.pdf(X))
# rvs
rvs = iw.rvs(size=sn)
args = (df/2, 0, 1./2)
alpha = 0.01
check_distribution_rvs('invgamma', args, alpha, rvs)
def test_is_scaled_chisquared(self):
# The 2-dimensional Wishart with an arbitrary scale matrix can be
# transformed to a scaled chi-squared distribution.
# For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
# :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
np.random.seed(482974)
sn = 500
df = 10
dim = 4
# Construct an arbitrary positive definite matrix
scale = np.diag(np.arange(4)+1)
scale[np.tril_indices(4, k=-1)] = np.arange(6)
scale = np.dot(scale.T, scale)
# Use :math:`\lambda = [1, \dots, 1]'`
lamda = np.ones((dim,1))
sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
w = wishart(df, sigma_lamda)
c = chi2(df, scale=sigma_lamda)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
X = np.linspace(0.1,10,num=10)
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df,0,sigma_lamda)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
def test_1D_is_chisquared(self):
# The 1-dimensional Wishart with an identity scale matrix is just a
# chi-squared distribution.
# Test variance, mean, entropy, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(1, 10, 2, dtype=float)
X = np.linspace(0.1,10,num=10)
for df in df_range:
w = wishart(df, scale)
c = chi2(df)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df,)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
def test_1D_is_invgamma(self):
# The 1-dimensional inverse Wishart with an identity scale matrix is
# just an inverse gamma distribution.
# Test variance, mean, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(5, 20, 2, dtype=float)
X = np.linspace(0.1, 10, num=10)
for df in df_range:
iw = invwishart(df, scale)
ig = invgamma(df / 2, scale=1. / 2)
# Statistics
assert_allclose(iw.var(), ig.var())
assert_allclose(iw.mean(), ig.mean())
# PDF
assert_allclose(iw.pdf(X), ig.pdf(X))
# rvs
rvs = iw.rvs(size=sn)
args = (df / 2, 0, 1. / 2)
alpha = 0.01
check_distribution_rvs('invgamma', args, alpha, rvs)
def test_is_scaled_chisquared(self):
# The 2-dimensional Wishart with an arbitrary scale matrix can be
# transformed to a scaled chi-squared distribution.
# For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
# :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
np.random.seed(482974)
sn = 500
df = 10
dim = 4
# Construct an arbitrary positive definite matrix
scale = np.diag(np.arange(4) + 1)
scale[np.tril_indices(4, k=-1)] = np.arange(6)
scale = np.dot(scale.T, scale)
# Use :math:`\lambda = [1, \dots, 1]'`
lamda = np.ones((dim, 1))
sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
w = wishart(df, sigma_lamda)
c = chi2(df, scale=sigma_lamda)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
X = np.linspace(0.1, 10, num=10)
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df, 0, sigma_lamda)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
def test_1D_is_chisquared(self):
# The 1-dimensional Wishart with an identity scale matrix is just a
# chi-squared distribution.
# Test variance, mean, entropy, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(1, 10, 2, dtype=float)
X = np.linspace(0.1, 10, num=10)
for df in df_range:
w = wishart(df, scale)
c = chi2(df)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df, )
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)