Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 245986, 23 pages
http://dx.doi.org/10.5402/2012/245986
Research Article

A Logistic -Moment-Based Analog for the Tukey - , , , and - System of Distributions

1Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, 222-J Wham Building, Carbondale, IL 62901-4618, USA
2Department of Curriculum and Instruction, University of Texas at Arlington, 320B Science Hall, Arlington, TX 76019, USA

Received 19 May 2012; Accepted 20 June 2012

Academic Editors: F. Fagnola, D. Fiems, and C. Proppe

Copyright © 2012 Todd C. Headrick and Mohan D. Pant. 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. Kysely and J. Picek, “Probability estimates of heavy precipitation events in a flood-prone central-European region with enhanced influence of Mediterranean cyclones,” Advances in Geosciences, vol. 12, no. 1, pp. 43–50, 2007. View at Google Scholar · View at Scopus
  2. K. Kochanek, W. Strupczewski, and V. P. Singh, “The PWM large quantile estimates of heavy tailed distributions from samples deprived of their largest element,” Hydrological Sciences Journal, vol. 53, no. 2, pp. 367–386, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. W. H. Asquith, Distributional Analysis with L-Moment Statistics Using the R Environment for Statistical Computing, Lubbock, Tex, USA, 2011.
  4. J. R. M. Hosking and J. R. Wallis, Regional Frequency Analysis: An Approach Based on L-Moments, Cambridge University Press, Cambridge, UK, 1997.
  5. B. Ghalebaz-Jeddi, G. L. Donohue, and J. F. Shortle, “A statistical analysis of the aircraft landing process,” Journal of Industrial and Systems Engineering, vol. 3, no. 3, pp. 152–169, 2009. View at Google Scholar
  6. V. Pisarenko and M. Rodkin, Heavy-Tailed Distributions in Disaster Analysis, Springer, New York, NY, USA, 2010.
  7. A. Ravi and F. B. Butar, “An insight into heavy-tailed distribution,” Journal of Mathematical Sciences and Mathematics Education, vol. 5, no. 1, 15 pages, 2010. View at Google Scholar
  8. A. Achim, E. E. Kuruoǧlu, and J. Zerubia, “SAR image filtering based on the heavy-tailed rayleigh model,” IEEE Transactions on Image Processing, vol. 15, no. 9, pp. 2686–2693, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. K. Yuan and P. M. Bentler, “Structural equation modeling with heavy tailed distributions,” Psychometrika, vol. 69, no. 3, pp. 421–436, 2004. View at Google Scholar · View at Scopus
  10. I. Berkovits, G. R. Hancock, and J. Nevitt, “Bootstrap resampling approaches for repeated measure designs: relative robustness to sphericity and normality violations,” Educational and Psychological Measurement, vol. 60, no. 6, pp. 877–892, 2000. View at Google Scholar · View at Scopus
  11. C. K. Enders, “The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data,” Psychological Methods, vol. 6, no. 4, pp. 352–370, 2001. View at Google Scholar · View at Scopus
  12. T. C. Headrick and S. S. Sawilowsky, “Simulating correlated multivariate nonnormal distributions: extending the fleishman power method,” Psychometrika, vol. 64, no. 1, pp. 25–35, 1999. View at Google Scholar · View at Scopus
  13. T. C. Headrick and S. S. Sawilowsky, “Properties of the rank transformation in factorial analysis of covariance,” Communications in Statistics, vol. 29, no. 4, pp. 1059–1087, 2000. View at Google Scholar · View at Scopus
  14. T. C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Chapman & Hall, Boca Raton, Fla, USA, 2010.
  15. J. W. Tukey, “Modern techniques in data analysis,” in Proceedings of the NSF-Sponsored Regional Research Conference, Southern Massachusetts University, Boston, Mass, USA, 1977.
  16. 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
  17. 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, pp. 449–462, 2008. View at Google Scholar
  18. 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 Google Scholar · View at Scopus
  19. C. Field and M. G. Genton, “The multivariate g-and-h distribution,” Technometrics, vol. 48, no. 1, pp. 104–111, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. R. K. Kowalchuk and T. C. Headrick, “Simulating multivariate g-and-h distributions,” British Journal of Mathematical and Statistical Psychology, vol. 63, no. 1, pp. 63–74, 2010. View at Publisher · View at Google Scholar · View at Scopus
  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
  22. J. R. M. Hosking, “L-moments: analysis and estimation of distributions using linear combinations of order statistics,” Journal of the Royal Statistical Society B, vol. 52, no. 1, pp. 105–124, 1990. View at Google Scholar · View at Zentralblatt MATH
  23. R. M. Vogel and N. M. Fennessey, “L-moment diagrams should replace product moment diagrams,” Water Resources Research, vol. 29, no. 6, pp. 1745–1752, 1993. View at Publisher · View at Google Scholar · View at Scopus
  24. F. A. Hodis, T. C. Headrick, and Y. Sheng, “Power method distributions through conventional moments and L-moments,” Applied Mathematical Sciences, vol. 6, no. 44, pp. 2159–2193, 2012. View at Google Scholar
  25. 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 Google Scholar
  26. K. P. Singh, C. M. S. Lee, and E. O. George, “On generalized log-logistic model for censored survival data,” Biometrical Journal, vol. 30, no. 7, pp. 843–850, 1988. View at Publisher · View at Google Scholar
  27. T. C. Headrick and M. D. Pant, “A method for simulating nonnormal distributions with specified L-Skew, L-Kurtosis, and L-Correlation,” ISRN Applied Mathematics, vol. 2012, Article ID 980827, 23 pages, 2012. View at Google Scholar
  28. M. C. Jones, “On some expressions for variance, covariance, skewness and L-moments,” Journal of Statistical Planning and Inference, vol. 126, no. 1, pp. 97–106, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. R. Serfling and P. Xiao, “A contribution to multivariate L-moments: L-comoment matrices,” Journal of Multivariate Analysis, vol. 98, no. 9, pp. 1765–1781, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. Wolfram Research Inc., Mathematica Version 8, Wolfram Research, Champaign, Ill, USA, 2010.
  31. G. Marsaglia, “Evaluating the normal distribution function,” Journal of Statistical Software, vol. 11, no. 5, pp. 1–11, 2004. View at Google Scholar · View at Scopus