HomeRecoletos Multidisciplinary Research Journalvol. 2 no. 2 (2014)

Transformation To Normality Based On Empirical Distribution Functions

Mark S. Borres | Efren O. Barabat

Discipline: Mathematics



The paper examines an efficient alternative to the Box-Cox and Yeo-Johnson’s transformation to normality procedures which works under very general conditions. The method hinges on two fundamental results : 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. Given two observations x and y, we computed Fn(x) and Fn(y) , which for large n, are approximately uniform random variables. These values are then inputted into the BoxMueller transformations. Bounds for the Kolmogorov-Smirnov statistic between the distribution of the transformed observations and the normal distribution are provided through numerical simulation and by appealing to the Dvoretzky-Kiefer-Wolfowitz inequality.