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

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.