Quantile Function - The Normal Distribution

The Normal Distribution

The normal distribution is perhaps the most important case. Because the normal distribution is a location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution, known as the probit function. Unfortunately, this function has no closed-form representation using basic algebraic functions; as a result, approximate representations are usually used. Thorough composite rational and polynomial approximations have been given by Wichura and Acklam (see his web site in External Links). Non-composite rational approximations have been developed by Shaw (see Monte Carlo recycling in External Links).