The probability functions for the Normal or Gaussian distribution are described in Abramowitz & Stegun, Section 26.2.
These routines compute the Gaussian probability density function Z(x) = (1/\sqrt{2\pi}) \exp(-x^2/2).
These routines compute the upper tail of the Gaussian probability function Q(x) = (1/\sqrt{2\pi}) \int_x^\infty dt \exp(-t^2/2).
The hazard function for the normal distribution, also known as the inverse Mills' ratio, is defined as, It decreases rapidly as x approaches -\infty and asymptotes to h(x) \sim x as x approaches +\infty.
These routines compute the hazard function for the normal distribution.