This paper derives closed-form solutions for the 𝑔-and-ℎ shape parameters associated with the Tukey family of distributions based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew and kurtosis functions. The MOP methodology is also extended from univariate to multivariate data generation. A procedure is described for simulating nonnormal distributions with specified Spearman correlations. TheMOP procedure has an advantage over theMOMbecause it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the proposedMOP procedure is superior to the MOM in terms of distribution fitting, estimation, relative bias, and relative error.
Kuo, Tzu C. and Headrick, Todd C. "Simulating Univariate and Multivariate Tukey g-and-h Distributions Based on the Method of Percentiles." (Jan 2014).