def E_tl_e_trunc_lower(tg, vare, o):
e_mu = 0.
ve = np.sqrt(vare)
b = o - tg
beta = (b - e_mu) / ve
return (e_mu - ve * np.exp(logpdf(beta) - logcdf(beta))) * cdf(
(o - tg - e_mu) / ve)
def E_tl_e_trunc_upper(tg, vare, o):
e_mu = 0.
ve = np.sqrt(vare)
alpha = (o - tg - e_mu) / ve
lambda_ = np.exp(logpdf(alpha) - logsf(alpha))
return (e_mu + ve * lambda_) * np.exp(logsf((o - tg - e_mu) / ve))
def _mean_truncnorm_ltail(b, mean=0., sd=1.):
beta = (b - mean) / sd
lphi_b = logpdf(beta)
lPhi_b = logcdf(beta)
return mean - sd * np.exp(lphi_b - lPhi_b)
def _var_truncnorm_rtail(a, mean=0., sd=1.):
alpha = (a - mean) / sd
lphi_a = logpdf(alpha)
lambda_ = np.exp(lphi_a - logsf(alpha))
return sd * sd * (1.0 - lambda_ * (lambda_ - alpha))
def _mean_truncnorm_rtail(a, mean=0., sd=1.):
alpha = (a - mean) / sd
return mean + sd * np.exp(logpdf(alpha) - logsf(alpha))