def _survival_function(self, params, times):
mu_, ln_sigma_, lambda_ = params
sigma_ = safe_exp(ln_sigma_)
Z = (log(times) - mu_) / sigma_
if lambda_ > 0:
return gammaincc(1 / lambda_ ** 2, safe_exp(lambda_ * Z - 2 * np.log(lambda_)))
else:
return gammainc(1 / lambda_ ** 2, safe_exp(lambda_ * Z - 2 * np.log(-lambda_)))
def _survival_function(self, params, times):
mu_, ln_sigma_, lambda_ = params
sigma_ = exp(ln_sigma_)
Z = (log(times) - mu_) / sigma_
if lambda_ > 0:
return gammaincc(1 / lambda_**2, exp(lambda_ * Z) / lambda_**2)
else:
return gammainc(1 / lambda_**2, exp(lambda_ * Z) / lambda_**2)
def _survival_function(self, params, T, Xs):
lambda_ = np.clip(Xs["lambda_"] @ params["lambda_"], 1e-25, 1e10)
sigma_ = safe_exp(Xs["sigma_"] @ params["sigma_"])
mu_ = Xs["mu_"] @ params["mu_"]
Z = (log(T) - mu_) / sigma_
ilambda_2 = 1 / lambda_ ** 2
exp_term = safe_exp(lambda_ * Z - 2 * log(np.abs(lambda_)))
return np.where(lambda_ > 0, gammaincc(ilambda_2, exp_term), gammainc(ilambda_2, exp_term))
def _survival_function(self, params, T, Xs):
lambda_ = Xs["lambda_"] @ params["lambda_"]
sigma_ = safe_exp(Xs["sigma_"] @ params["sigma_"])
mu_ = Xs["mu_"] @ params["mu_"]
Z = (log(T) - mu_) / sigma_
ilambda_2 = 1 / lambda_**2
exp_term = np.clip(safe_exp(lambda_ * Z) * ilambda_2, 1e-300, 1e25)
return np.where(lambda_ > 0, gammaincc(ilambda_2, exp_term),
gammainc(ilambda_2, exp_term))
def _survival_function(self, params, times):
mu_, ln_sigma_, lambda_ = params
sigma_ = safe_exp(ln_sigma_)
Z = (log(times) - mu_) / sigma_
clipped_exp = np.clip(safe_exp(lambda_ * Z) / lambda_**2, 1e-15, 1e20)
ilambda_2 = 1 / lambda_**2
if lambda_ > 0:
v = gammaincc(ilambda_2, clipped_exp)
elif lambda_ < 0:
v = gammainc(ilambda_2, clipped_exp)
else:
v = norm.sf(Z)
# never return a 0
return np.clip(v, 1e-50, 1 - 1e-50)
def test_a_special_case_of_the_derivative():
"""
We know a specific to test against:
dUIG(s, x) / ds at (s=1, x) = ln(x) * UIG(1, x) + E_1(x)
where E_1(x) is the exponential integral
"""
# incomplete upper gamma
IUG = lambda s, x: gammaincc(s, x) * gamma(s)
def analytical_derivative(x):
dIUG = np.log(x) * IUG(1., x) - expi(-x)
return dIUG
def approx_derivative(x):
return jacobian(IUG, argnum=0)(1., x)
x = np.linspace(1, 12)
npt.assert_allclose(analytical_derivative(x), approx_derivative(x))
x = np.logspace(-25, 25, 100)
npt.assert_allclose(analytical_derivative(x), approx_derivative(x))
