def test_skewstudent(self):
dist = SkewStudent()
eta, lam = 4.0, .5
ll1 = dist.loglikelihoood(np.array([eta, lam]),
self.resids, self.sigma2)
# Direct calculation of PDF, then log
const_c = gamma((eta+1)/2) / ((np.pi*(eta-2))**.5 * gamma(eta/2))
const_a = 4*lam*const_c*(eta-2)/(eta-1)
const_b = (1 + 3*lam**2 - const_a**2)**.5
resids = self.resids / self.sigma2**.5
pdf = const_b * const_c / self.sigma2**.5 \
* (1 + 1/(eta-2) *((const_b * resids + const_a)
/(1 + np.sign(resids + const_a / const_b) * lam))**2)**(-(eta+1)/2)
ll2 = np.log(pdf).sum()
assert_almost_equal(ll1, ll2)
assert_equal(dist.num_params, 2)
bounds = dist.bounds(self.resids)
assert_equal(len(bounds), 2)
A, b = dist.constraints()
assert_equal(A.shape, (4, 2))
k = stats.kurtosis(self.resids, fisher=False)
sv = max((4.0 * k - 6.0) / (k - 3.0) if k > 3.75 else 12.0, 4.0)
assert_array_equal(dist.starting_values(self.resids), np.array([sv, 0.]))
assert_raises(ValueError, dist.simulate, np.array([1.5, 0.]))
assert_raises(ValueError, dist.simulate, np.array([4., 1.5]))
assert_raises(ValueError, dist.simulate, np.array([4., -1.5]))
assert_raises(ValueError, dist.simulate, np.array([1.5, 1.5]))
def test_skewstudent(self):
dist = SkewStudent()
eta, lam = 4.0, .5
ll1 = dist.loglikelihood(np.array([eta, lam]), self.resids,
self.sigma2)
# Direct calculation of PDF, then log
const_c = gamma(
(eta + 1) / 2) / ((np.pi * (eta - 2))**.5 * gamma(eta / 2))
const_a = 4 * lam * const_c * (eta - 2) / (eta - 1)
const_b = (1 + 3 * lam**2 - const_a**2)**.5
resids = self.resids / self.sigma2**.5
pow = (-(eta + 1) / 2)
pdf = const_b * const_c / self.sigma2 ** .5 * \
(1 + 1 / (eta - 2) *
((const_b * resids + const_a) /
(1 + np.sign(resids + const_a / const_b) * lam)) ** 2) ** pow
ll2 = np.log(pdf).sum()
assert_almost_equal(ll1, ll2)
assert_equal(dist.num_params, 2)
bounds = dist.bounds(self.resids)
assert_equal(len(bounds), 2)
a, b = dist.constraints()
assert_equal(a.shape, (4, 2))
k = stats.kurtosis(self.resids, fisher=False)
sv = max((4.0 * k - 6.0) / (k - 3.0) if k > 3.75 else 12.0, 4.0)
assert_array_equal(dist.starting_values(self.resids),
np.array([sv, 0.]))
with pytest.raises(ValueError):
dist.simulate(np.array([1.5, 0.]))
with pytest.raises(ValueError):
dist.simulate(np.array([4., 1.5]))
with pytest.raises(ValueError):
dist.simulate(np.array([4., -1.5]))
with pytest.raises(ValueError):
dist.simulate(np.array([1.5, 1.5]))
