ON THE FOURTH ROOT TRANSFORMATION OF CHI‐SQUARE

Abstract

SummaryWe show that, within the family of power transformations of a Chisquare variable, the square and fourth roots minimize Pearson's index of kurtosis. Two new transtormations of the fourth root, a symmetrized‐truncated version and its linear combination with the square root are also studied. The first transformation shows a considerable improvement over the fourth root while the second one turns out to be even more accurate than Hilferty‐Wilson's cube root transformation.