Table of Contents
ISRN Probability and Statistics
Volume 2014, Article ID 645823, 10 pages
http://dx.doi.org/10.1155/2014/645823
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.

Linked References

  1. J. Algina, H. J. Keselman, and R. D. Penfield, “Confidence interval coverage for Cohen's effect size statistic,” Educational and Psychological Measurement, vol. 66, no. 6, pp. 945–960, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  2. J. Algina, H. J. Keselman, and R. D. Penfield, “Confidence intervals for an effect size when variances are not equal,” Journal of Modern Applied Statistical Methods, vol. 5, pp. 2–13, 2006. View at Google Scholar
  3. S. G. Badrinath and S. Chatterjee, “A data-analytic look at skewness and elongation in common-stock return distributions,” Journal of Business and Economic Statistics, vol. 9, pp. 223–233, 1991. View at Google Scholar
  4. D. J. Dupuis and C. A. Field, “Large wind speeds: modeling and outlier detection,” Journal of Agricultural, Biological, and Environmental Statistics, vol. 9, pp. 105–121, 2004. View at Google Scholar
  5. C. Field and M. G. Genton, “The multivariate g-and-h distribution distribution,” Technometrics, vol. 48, no. 1, pp. 104–111, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. G. M. Goerg, The Lambert Way to Gaussianize skewed, heavy tailed data with the inverse of Tukey's h transformation as a special case [Ph.D. thesis], Cornell University, 2011.
  7. D. Guegan and B. Hassani, “A modified Panjer algorithm for operational risk capital calculations,” Journal of Operational Risk, vol. 4, pp. 53–72, 2009. View at Google Scholar
  8. T. C. Headrick, R. K. Kowalchuk, and Y. Sheng, “Parametric probability densities and distribution functions for Tukey g-and-h transformations and their use for fitting data,” Applied Mathematical Sciences, vol. 2, no. 9–12, pp. 449–462, 2008. View at Google Scholar · View at MathSciNet
  9. D. C. Hoaglin, F. Mosteller, and J. W. Tukey, Summarizing Shape Numerically: the g-and-h Distributions, Wiley, New York, NY, USA, 1985.
  10. R. K. Kowalchuk and T. C. Headrick, “Simulating multivariate g-and-h distributions,” The British Journal of Mathematical and Statistical Psychology, vol. 63, no. 1, pp. 63–74, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. J. Keselman, R. K. Kowalchuk, and L. M. Lix, “Robust nonorthogonal analyses revisited: an update based on trimmed means,” Psychometrika, vol. 63, pp. 145–163, 1998. View at Google Scholar
  12. H. J. Keselman, L. M. Lix, and R. K. Kowalchuk, “Multiple comparison procedures for trimmed means,” Psychological Methods, vol. 3, pp. 123–141, 1998. View at Google Scholar
  13. J. Martinez and B. Iglewicz, “Some properties of the Tukey g-and-h family of distributions,” Communications in Statistics A, vol. 13, no. 3, pp. 353–369, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Morgenthaler and J. W. Tukey, “Fitting quantiles: doubling, HR, HQ, and HHH distributions,” Journal of Computational and Graphical Statistics, vol. 9, no. 1, pp. 180–195, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. W. Tukey, “Modern techniques in data analysis,” in NSF Sponsored Regional Research Conference at Southern Massachusetts University, North Dartmouth, Mass, USA, 1977.
  16. R. R. Wilcox, “Comparing the slopes of two independent regression lines when there is complete heteroscedasticity,” British Journal of Mathematical and Statistical Psychology, vol. 50, pp. 309–317, 1997. View at Google Scholar
  17. R. R. Wilcox, “Detecting nonlinear associations, plus comments on testing hypotheses about the correlation coefficient,” Journal of Educational and Behavioral Statistics, vol. 26, pp. 73–83, 2001. View at Google Scholar
  18. D. C. Hoaglin, Encyclopedia of Statistical Sciences, Wiley, New York, NY, USA, 1983.
  19. F. A. Hodis, T. C. Headrick, and Y. Sheng, “Power method distributions through conventional moments and L-moments,” Applied Mathematical Sciences, vol. 6, no. 41-44, pp. 2159–2193, 2012. View at Google Scholar · View at MathSciNet
  20. T. C. Headrick, “A characterization of power method transformations through L-moments,” Journal of Probability and Statistics, vol. 2011, Article ID 497463, 22 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. T. C. Headrick and M. D. Pant, “Characterizing Tukey h and hh-distributions through L-moments and the L-correlation,” ISRN Applied Mathematics, vol. 2012, Article ID 980153, 20 pages, 2012. View at Google Scholar · View at MathSciNet
  22. T. C. Headrick and M. D. Pant, “Simulating non-normal distributions with specified L-moments and L-correlations,” Statistica Neerlandica, vol. 66, no. 4, pp. 422–441, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  23. M. D. Pant and T. C. Headrick, “A method for simulating Burr Type III and Type XII distributions through L-moments and L- correlations,” ISRN Applied Mathematics, vol. 2013, Article ID 191604, 14 pages, 2013. View at Google Scholar
  24. Z. A. Karian and E. J. Dudewicz, “Comparison of gld fitting methods: superiority of percentile fits to moments in L2 norm,” Journal of the Iranian Statistical Society, vol. 2, pp. 171–187, 2003. View at Google Scholar
  25. E. J. Dudewicz and Z. A. Karian, “Fitting the generalized lambda distribution (GLD) system by a method of percentiles, II: tables,” American Journal of Mathematical and Management Sciences, vol. 19, pp. 1–73, 1999. View at Google Scholar
  26. Z. A. Karian and E. J. Dudewicz, “Fitting the generalized lambda distribution to data: a method based on percentiles,” Communications in Statistics: Simulation and Computation, vol. 28, pp. 793–819, 1999. View at Google Scholar
  27. Z. A. Karian and E. J. Dudewicz, Handbook of Fitting Statistical Distributions with R, Chapman & Hall, 2011. View at MathSciNet
  28. T. C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Chapman & Hall/CRC, 2010.
  29. IBM Corp. IBM SPSS Statistics for Windows, version 20.0. Armonk, NY, USA, IBM Corp., 2011.
  30. T. C. Headrick and M. D. Pant, “On the order statistics of standard normal-based power method distributions,” ISRN Applied Mathematics, vol. 2012, Article ID 945627, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. N. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, John Wiley, New York, NY, USA, 1994.
  32. P. A. P. Moran, “Rank correlation and product-moment correlation,” Biometrika, vol. 35, pp. 203–206, 1948. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. TIBCO Software, TIBCO Spotfire S+ 8.1 for Windows, Palo Alto, Calif, USA, 2008.