Quadratic radical function better than fisher z transformation

Abstract

A new explicit quadratic radical function is found by numerical experiments, which is simpler and has only 70.778% of the maximal distance error compared with the Fisher z transformation. Furthermore, a piecewise function is constructed for the standard normal distribution: if the independent variable falls in the interval (−1.519, 1.519), the proposed function is employed; otherwise, the Fisher z transformation is used. Compared with the Fisher z transformation, this piecewise function has only 38.206% of the total error. The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.

Keywords

normal distribution / cumulative distribution function / error function / confidence interval / correlation coefficient / combination of forecasts

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