DOI: https://doi.org/10.14710/jfma.v8i1.20508

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

*Louie Resti Sandoval Rellon orcid scopus  -  University of Mindanao, Philippines

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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.

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Keywords: transformation to normality, Box-Cox method, Johnson method, inequalities

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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