Quadratic radical function better than fisher z transformation FIG 3

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.