def normal_lccdf(mu, sigma, x):
z = (x - mu) / sigma
return aet.switch(
aet.gt(z, 1.0),
aet.log(aet.erfcx(z / aet.sqrt(2.0)) / 2.0) - aet.sqr(z) / 2.0,
aet.log1p(-aet.erfc(-z / aet.sqrt(2.0)) / 2.0),
)
def normal_lcdf(mu, sigma, x):
"""Compute the log of the cumulative density function of the normal."""
z = (x - mu) / sigma
return aet.switch(
aet.lt(z, -1.0),
aet.log(aet.erfcx(-z / aet.sqrt(2.0)) / 2.0) - aet.sqr(z) / 2.0,
aet.log1p(-aet.erfc(z / aet.sqrt(2.0)) / 2.0),
)
def invprobit(x):
return 0.5 * erfc(-x / sqrt(2.0))
