Section 4   Application to Major Distribution Functions

An important application of the "$h$" function is to unify many distribution functions that do not have a closed-form expression. In this section, I present an extensive study that applies "$h$" to explicitly specify and evaluate those functions. I start by discussing the question of numerical precision, and then provides a series of applications to various families of distributions, including those related to the gamma function, the exponential integral function, the error function, the beta function, the hypergeometric function, the Marcum $Q$-function, and the truncated normal distribution.

Download [full paper] [supplementary materials] [.m files] [technical note]