An Algorithm for Generalized Conversion to Normal Distribution for Independent and Identically Distributed Random Variables

Abstract

The paper analyzes an efficient alternative to the Box-Cox and Johnson’s transformation to normality methods which operates under fairly general settings. The method hinges on two results in mathematical statistics: the fact that the cumulative distribution function F(x) of a random variable x always has a U(0,1) distribution and the Box-Mueller transformation of uniform random variables to standard normal random variables.  Bounds for the Kolmogorov-Smirnov statistic between the distribution of the transformed observations and the normal distribution are provided by numerical simulation and by appealing to the Dvoretzky-Kiefer- Wolfowitz inequality