def estimate_bivariate_mle_jr():
ndim = 2
size = (10000, ndim)
data = np.random.normal(size=size)
eta, lam = 4, -.9
skst = SkewStudent(eta=eta, lam=lam)
data = skst.rvs(size=size)
model = SkStJR(ndim=ndim, data=data)
out = model.fit_mle()
print(out)
model.from_theta(out.x)
fig, axes = plt.subplots(nrows=size[1], ncols=1)
for innov, ax in zip(data.T, axes):
sns.kdeplot(innov, ax=ax, label='data')
lines = [ax.get_lines()[0].get_xdata() for ax in axes]
lines = np.vstack(lines).T
marginals = model.marginals(lines)
for line, margin, ax in zip(lines.T, marginals.T, axes):
ax.plot(line, margin, label='fitted')
ax.legend()
plt.show()
def test_rvs(self):
"""Test simulation."""
eta, lam = [10, 15, 10], [.5, 1.5, 2]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
size = 10
rvs = skst.rvs(size=size)
self.assertEqual(rvs.shape, (size, len(lam)))
def test_pdf(self):
"""Test pdf."""
eta, lam = [10, 15, 10], [.5, 1.5, 2]
skst = SkStJR(eta=eta, lam=lam, ndim=len(lam))
size = (10, len(eta))
data = np.random.normal(size=size)
pdf = skst.pdf(data)
self.assertEqual(pdf.ndim, 1)
self.assertEqual(pdf.shape, (size[0], ))
def test_marginals(self):
"""Test marginals."""
eta, lam = [10, 15, 10], [.5, 1.5, 2]
skst = SkStJR(eta=eta, lam=lam, ndim=len(lam))
size = (10, len(eta))
data = np.random.normal(size=size)
marginals = skst.marginals(data)
self.assertEqual(marginals.ndim, 2)
self.assertEqual(marginals.shape, size)
self.assertGreater(marginals.all(), 0)
def test_init(self):
"""Test __init__."""
skst = SkStJR(ndim=3)
self.assertIsInstance(skst.eta, np.ndarray)
self.assertIsInstance(skst.lam, np.ndarray)
eta, lam = [10, 15], [.5, 1.5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
npt.assert_array_equal(skst.eta, np.array(eta))
npt.assert_array_equal(skst.lam, np.array(lam))
eta, lam = [15, 10], [1.5, .5]
skst.from_theta(np.concatenate((eta, lam)))
npt.assert_array_equal(skst.eta, np.array(eta))
npt.assert_array_equal(skst.lam, np.array(lam))
size = (10, len(eta))
data = np.random.normal(size=size)
skst = SkStJR(ndim=len(lam), data=data)
npt.assert_array_equal(skst.data, data)
def test_likelihood(self):
"""Test log-likelihood."""
eta, lam = [10, 15, 10], [.5, 1.5, 2]
theta = np.concatenate((eta, lam))
size = (10, len(eta))
data = np.random.normal(size=size)
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam, data=data)
logl1 = skst.likelihood(theta)
logl2 = skst.likelihood(theta * 2)
self.assertIsInstance(logl1, float)
self.assertNotEqual(logl1, logl2)
npt.assert_array_equal(skst.data, data)
def compute_quantile():
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
eta, lam = 20, 1.5
skst = SkStBL(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
eta, lam = 100, 1.5
skst = SkStDM(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
def plot_bidensity():
lam = [1.5, -2]
mvsn = MvSN(ndim=len(lam), lam=lam)
mvsn.plot_bidensity()
eta = 20
skst = MvSt(ndim=2, eta=eta)
skst.plot_bidensity()
eta, lam = [20, 5], [1.5, .5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
eta, lam = 20, [1.5, .5]
skst = SkStBL(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
eta, lam = 20, [1.5, -2]
skst = SkStDM(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
eta, lam = 20, [1.5, -2]
skst = SkStAC(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
def compute_quantile():
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
eta, lam = 20, 1.5
skst = SkStBL(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
eta, lam = 100, 1.5
skst = SkStDM(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1) - 2)
print(skst.ppf(cdf))
def estimate_bivariate_mle_jr():
ndim = 2
size = (10000, ndim)
data = np.random.normal(size=size)
eta, lam = 4, -.9
skst = SkewStudent(eta=eta, lam=lam)
data = skst.rvs(size=size)
model = SkStJR(ndim=ndim, data=data)
out = model.fit_mle()
print(out)
model.from_theta(out.x)
fig, axes = plt.subplots(nrows=size[1], ncols=1)
for innov, ax in zip(data.T, axes):
sns.kdeplot(innov, ax=ax, label='data')
lines = [ax.get_lines()[0].get_xdata() for ax in axes]
lines = np.vstack(lines).T
marginals = model.marginals(lines)
for line, margin, ax in zip(lines.T, marginals.T, axes):
ax.plot(line, margin, label='fitted')
ax.legend()
plt.show()
def compute_univ_cdf():
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1)))
eta, lam = 20, 1.5
skst = SkStBL(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1)))
eta, lam = 100, 1.5
skst = SkStDM(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1) + 10))
def compute_cdf():
eta, lam = [20, 5], [1.5, .5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
eta, lam = 20, [1.5, .5]
skst = SkStBL(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
eta, lam = 100, [1.5, -2]
skst = SkStDM(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
def compute_univ_cdf():
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1)))
eta, lam = 20, 1.5
skst = SkStBL(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1)))
eta, lam = 100, 1.5
skst = SkStDM(ndim=1, eta=eta, lam=lam)
print(skst.cdf(np.zeros(1)+10))
def compute_cdf():
eta, lam = [20, 5], [1.5, .5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
eta, lam = 20, [1.5, .5]
skst = SkStBL(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
eta, lam = 100, [1.5, -2]
skst = SkStDM(ndim=len(lam), eta=eta, lam=lam)
print(skst.cdf(np.zeros(2)))
def test_cdf(self):
"""Test cdf."""
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(1))
self.assertIsInstance(cdf, float)
eta, lam = [20, 5], [1.5, .5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
cdf = skst.cdf(np.zeros(2) - 10)
self.assertIsInstance(cdf, float)
def test_quantile(self):
"""Test quantile."""
eta, lam = 20, 1.5
skst = SkStJR(ndim=1, eta=eta, lam=lam)
arg = -2.
cdf = skst.cdf(arg)
ppf = skst.ppf(cdf)
self.assertAlmostEqual(ppf, arg)
arg = -.1 * np.ones(3)
cdf = skst.cdf_vec(arg)
quantiles = skst.ppf_vec(cdf)
npt.assert_array_almost_equal(arg, quantiles)
def plot_bidensity_simulated():
size = int(1e4)
lam = [1.5, -2]
mvsn = MvSN(ndim=len(lam), lam=lam)
mvsn.plot_bidensity()
rvs = mvsn.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
eta = 20
skst = MvSt(ndim=2, eta=eta)
skst.plot_bidensity()
rvs = skst.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
eta, lam = [20, 5], [1.5, .5]
skst = SkStJR(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
rvs = skst.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
eta, lam = 20, [1.5, .5]
skst = SkStBL(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
rvs = skst.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
eta, lam = 20, [1.5, -2]
skst = SkStDM(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
rvs = skst.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
eta, lam = 20, [1.5, -2]
skst = SkStAC(ndim=len(lam), eta=eta, lam=lam)
skst.plot_bidensity()
rvs = skst.rvs(size=size)
sns.kdeplot(rvs, shade=True)
plt.axis('square')
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.show()
