Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions

By Todd C. Headrick. 2002

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Testing the significance of a correlation with nonnormal data: comparison of Pearson, Spearman, transformation, and resampling approaches. (2012, background): “In contrast, other algorithms are limited in the combinations of skewness, kurtosis, or other moments that they can produce, and they can be especially limited for generating bimodal data (Headrick, 2002; Headrick & Sawilowsky, 1999, 2000).”
Best Alternatives to Cronbach's Alpha Reliability in Realistic Conditions: Congeneric and Asymmetrical Measurements (2016, methodology): “Skewed items: Standard normal Xij were transformed to generate non-normal distributions using the procedure proposed by Headrick (2002) applying fifth order polynomial transforms:”
Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. (2016, methodology): “We used a fifth-order polynomial transformation method for generating the correlated non-normally distributed variables (Headrick, 2002).”
Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation (2014, methodology): “1, due to the ability to control higher order moments, the NPNT can accommodate the irregular distribution which is difficult for TPNT and FPNT.”