Transformation of an empirical distribution to normal distribution by the use of Johnson system of translation and symmetrical quantile method

TRANSFORMACE EMPIRICKÉHO ROZDĚLENÍ NA NORMÁLNÍ ROZDĚLENÍ S POUŽITÍM JOHNSONOVY TRANSFORMACE A METODY SYMETRICKÝCH KVANTILŮ

Ludvík Friebel and Jana Friebelová
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Ludvík Friebel: University of South Bohemia in České Budějovice
Jana Friebelová: University of South Bohemia in České Budějovice

Acta Universitatis Bohemiae Meridionalis, 2006, vol. 9, issue 1, 75-79

Abstract: This article deals with approximation of empirical distribution to standard normal distribution using Johnson transformation. This transformation enables us to approximate wide spectrum of continuous distributions with a normal distribution. The estimation of parameters of transformation formulas is based on percentiles of empirical distribution. There are derived theoretical probability distribution functions of random variable obtained on the base of backward transformation standard normal distribution in the paper. The Method is introduced on practical example.

Keywords: standard normal distribution; empirical distribution; random variable; probability density function; cumulative distribution function; inverse cumulative distribution function; histogram; Johnson translation; location parameter; range parameter; shape parameter; bounded distribution; unbounded distribution; curve fitting; percentile (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:boh:actaub:v:9:y:2006:i:1:p:75-79

DOI: 10.32725/acta.2006.011

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