The Wilson-Hilferty Transformation
A 95-year-old cube root that turns a lopsided chi-square into something almost perfectly Normal
Wilson and Hilferty's 1931 cube-root normalizing transformation turns a skewed chi-square variable into something very close to standard Normal -- a refinement of Fisher's earlier square-root approximation. This article derives the transformation from a power-family expansion, uses exact symbolic algebra to prove that the cube root is the unique power that cancels the leading-order skewness term, verifies its accuracy against the exact chi-square distribution and against Fisher's approximation, and extends the same argument to the general Gamma distribution.
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