def test_ev_copula_distr(case):
# check ev copulas, cdf and transform against R `evd` package
ev_tr, v1, v2, args, res1 = case
u = [v1, v2]
res = copula_bv_ev(u, ev_tr, args=args)
assert_allclose(res, res1, rtol=1e-13)
ev = ExtremeValueCopula(ev_tr)
cdf1 = ev.cdf(u, args)
assert_allclose(cdf1, res1, rtol=1e-13)
cev = CopulaDistribution([uniform, uniform], ev, copargs=args)
cdfd = cev.cdf(np.array(u), args=args)
assert_allclose(cdfd, res1, rtol=1e-13)
assert cdfd.shape == ()
# using list u
cdfd = cev.cdf(u, args=args)
assert_allclose(cdfd, res1, rtol=1e-13)
assert cdfd.shape == ()
# check vector values for u
# bilogistic is not vectorized, uses integrate.quad
if ev_tr != trev.transform_bilogistic:
cdfd = cev.cdf(np.array(u) * np.ones((3, 1)), args=args)
assert_allclose(cdfd, res1, rtol=1e-13)
assert cdfd.shape == (3, )
def test_ev_copula(case):
# check ev copulas, cdf and transform against R `evd` package
ev_tr, v1, v2, args, res1 = case
res = copula_bv_ev([v1, v2], ev_tr, args=args)
assert_allclose(res, res1, rtol=1e-13)
# check derivatives of dependence function
if ev_tr in (trev.transform_bilogistic, trev.transform_tev):
return
d1_res = approx_fprime_cs(np.array([v1, v2]), ev_tr.evaluate, args=args)
d1_res = np.diag(d1_res)
d1 = ev_tr.deriv(np.array([v1, v2]), *args)
assert_allclose(d1, d1_res, rtol=1e-8)
d1_res = approx_hess(np.array([0.5]), ev_tr.evaluate, args=args)
d1_res = np.diag(d1_res)
d1 = ev_tr.deriv2(0.5, *args)
assert_allclose(d1, d1_res, rtol=1e-7)
def test_gev_genextreme(case):
gev = stats.genextreme(0)
# check ev copulas, cdf and transform against R `evt` package
ev_tr, v1, v2, args, res0, res1, res2 = case
y = [v1, v2]
u = gev.cdf(y)
res = copula_bv_ev(u, ev_tr, args=args)
assert_allclose(res, res1, rtol=1e-13)
ev = ExtremeValueCopula(ev_tr)
# evaluated at using u = y
cdf1 = ev.cdf(y, args)
assert_allclose(cdf1, res0, rtol=1e-13)
# evaluated at transformed u = F(y)
cdf1 = ev.cdf(u, args)
assert_allclose(cdf1, res1, rtol=1e-13)
cev = CopulaDistribution([gev, gev], ev, copargs=args)
cdfd = cev.cdf(np.array(y), args=args)
assert_allclose(cdfd, res1, rtol=1e-13)
pdfd = cev.pdf(np.array(y), args=args)
assert_allclose(pdfd, res2, rtol=1e-13)