Transformation To Normality Based On Empirical Distribution Functions

Authors

  • Mark S. Borres University of San Jose-Recoletos
  • Efren O. Barabat University of San Jose-Recoletos

DOI:

https://doi.org/10.32871/rmrj1402.02.12

Keywords:

transformation to normality, Box-Cox method, Johnson method, inequalities, Dvoretzky-Kiefer-Wolfowitz

Abstract

The paper examines an effi cient 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 Box-Mueller 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.

Author Biographies

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges. Currently, he is one of the Research Staff of CPRDS doing research on Fractal Statistics and Fractal Geometry and also assumes the position of Secretary in the Recoletos Multidisciplinary Research Journal.

Efren O. Barabat, University of San Jose-Recoletos

an Electronics Engineer, graduated from the University of San Jose-Recoletos in 2010, Cum Laude honors. He ranked as top 9 examinee in the April 2011 ECE Licensure Examination. He worked as Field Engineer in SMART Communications, Inc. from 2011 to 2012. Currently, a full-time faculty member of the Electronics Engineering Department of USJ-R College of Engineering, handling Mathematics and Major Subjects of ECE.

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Published

2014-12-28

How to Cite

Borres, M. S., & Barabat, E. O. (2014). Transformation To Normality Based On Empirical Distribution Functions. Recoletos Multidisciplinary Research Journal, 2(2). https://doi.org/10.32871/rmrj1402.02.12

Issue

Vol. 2 No. 2 (2014)

Section

Articles

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Copyright of the Journal belongs to the University of San Jose-Recoletos

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