Table of Contents
ISRN Probability and Statistics
Volume 2014, Article ID 645823, 10 pages
Research Article

Simulating Univariate and Multivariate Tukey -and- Distributions Based on the Method of Percentiles

Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, P.O. Box 4618, 222-J Wham Building, Carbondale, IL 62901-4618, USA

Received 2 October 2013; Accepted 19 November 2013; Published 12 January 2014

Academic Editors: M. Campanino, X. Dang, and J. Villarroel

Copyright © 2014 Tzu Chun Kuo and Todd C. Headrick. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper derives closed-form solutions for the -and- 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. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the proposed MOP procedure is superior to the MOM in terms of distribution fitting, estimation, relative bias, and relative error.