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Edwin Bidwell Wilson was a mathematician and statistician, remembered in statistics for the Wilson score interval. His 1931 paper with Margaret M. Hilferty introduced an influential approximation to the chi-squared distribution. His firsthand National Academy of Sciences memoir lists the paper under his full name.^[ref]

Their Wilson-Hilferty transformation uses $(X/k{)}^{1/3}$ for a chi-squared distribution with $k$ statistical degrees of freedom. Its approximate mean $1-2/(9k)$ and variance $2/(9k)$ give a normal approximation useful for converting quantiles between the two distributions.^[ref]

Margaret M. Hilferty coauthored the 1931 paper The Distribution of Chi-Square by Edwin B. Wilson and Margaret M. Hilferty. The original byline identifies her with Harvard's Department of Vital Statistics; no fuller personal name is inferred from the initials.^[ref]

Their Wilson-Hilferty transformation reduces the skewness of a chi-squared distribution by taking a cube root. For $X\sim {\chi }_k^2$, the standardized quantity $((X/k{)}^{1/3}-(1-2/(9k)))/\sqrt{2/(9k)}$ is approximately standard normal. It provides a practical approximation to quantiles and tail probabilities, with accuracy depending on the statistical degrees of freedom and the probability region.^[ref]

By Edwin B. Wilson and Margaret M. Hilferty. Proceedings of the National Academy of Sciences 17(12), 684–688 (1931). DOI: doi.org/10.1073/pnas.17.12.684

Full text: pmc.ncbi.nlm.nih.gov/articles/PMC1076144/

Locator: pp. 684–688, cube-root approximation to the chi-square distribution.