Fast probability integration by three-parameter normal tail approximation

A new method of fast probability integration is presented, based on a three-parameter normal tail approximation to a non-normal distribution function. Values of the distribution function, the probability density function and its derivative are matched at the approximation point with the approximating function. The approximation point is the known “design point”, used within the framework of second moment reliability theory. The proposed method is as fast as the available two-parameter algorithm, but is apparently more accurate.