- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 980827, 23 pages
A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation
1Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, 222-J Wham Bldg, Carbondale, IL 62901-4618, USA
2Department of Curriculum and Instruction, University of Texas at Arlington, 320B Science Hall, Arlington, TX 76019, USA
Received 21 February 2012; Accepted 15 May 2012
Academic Editors: J. R. Fernandez, E. Skubalska-Rafajlowicz, and W. Yeih
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.
- A. I. Fleishman, “A method for simulating non-normal distributions,” Psychometrika, vol. 43, no. 4, pp. 521–532, 1978.
- T. C. Headrick, “Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions,” Computational Statistics & Data Analysis, vol. 40, no. 4, pp. 685–711, 2002.
- T. C. Headrick, Statistical Simulation: Power Method Polynomials and other Tranformations, Chapman and Hall/CRC, Boca Raton, Fla, USA, 2010.
- J. S. Ramberg and B. W. Schmeiser, “An approximate method for generating asymmetric random variables,” Communications of the ACM, vol. 17, pp. 78–82, 1974.
- J. S. Ramberg, E. J. Dudewicz, P. R. Tadikamalla, and E. F. Mykytka, “A probability distribution and its uses in fitting data,” Technometrics, vol. 21, no. 2, pp. 201–214, 1979.
- Z. A. Karian and E. J. Dudewicz, Handbook of Fitting Statistical Distributions with R, Chapman and Hall/CRC Press, Boca Raton, Fla, USA, 2011.
- J. R. M. Hosking, “-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.
- J. R. M. Hosking and J. R. Wallis, Regional Frequency Analysis: An Approach Based on L-Moments, Cambridge University Press, Cambridge, UK, 1997.
- 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.
- F. A. Hodis, T. C. Headrick, and Y. Sheng, “Power method distributions through conventional moments and Lmoments,” Applied Mathematical Sciences, vol. 6, no. 44, pp. 2159–2193, 2012.
- T. C. Headrick, “A characterization of power method transformations through -moments,” Journal of Probability and Statistics, vol. 2011, Article ID 497463, 22 pages, 2011.
- W. H. Asquith, “Lmoments and TL-moments of the generalized lambda distribution,” Computational Statistics & Data Analysis, vol. 51, no. 9, pp. 4484–4496, 2007.
- J. Karvanen and A. Nuutinen, “Characterizing the generalized lambda distribution by -moments,” Computational Statistics & Data Analysis, vol. 52, no. 4, pp. 1971–1983, 2008.
- C. D. Vale and V. A. Maurelli, “Simulating multivariate nonnormal distributions,” Psychometrika, vol. 48, no. 3, pp. 465–471, 1983.
- 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.
- C. J. Corrado, “Option pricing based on the generalized lambda distribution,” Journal of Future Markets, vol. 21, no. 3, pp. 213–236, 2001.
- T. C. Headrick and A. Mugdadi, “On simulating multivariate non-normal distributions from the generalized lambda distribution,” Computational Statistics & Data Analysis, vol. 50, no. 11, pp. 3343–3353, 2006.
- R. Serfling and P. Xiao, “A contribution to multivariate -moments: -comoment matrices,” Journal of Multivariate Analysis, vol. 98, no. 9, pp. 1765–1781, 2007.
- T. C. Headrick and M. D. Pant, “Characterizing Tukey h and hh-distributions through Lmoments and the Lcorrelation,” ISRN Applied Mathematics, vol. 2012, Article ID 980153, 20 pages, 2012.
- M. C. Jones, “On some expressions for variance, covariance, skewness and -moments,” Journal of Statistical Planning and Inference, vol. 126, no. 1, pp. 97–106, 2004.
- Wolfram Research, Mathematica, Version 8.0, Wolfram Research, Champaign, Ill, USA, 2010.
- G. Marsaglia, “Evaluating the normal distribution,” Journal of Statistical Software, vol. 11, no. 5, pp. 1–11, 2004.
- TIBCO Spotfire S+ 8.1 for Windows, TIBCO Software, Palo Alto, Calif, USA, 2008.
- T. C. Headrick, R. K. Kowalchuk, and Y. Sheng, “Parametric probability densities and distribution functions for Tukey -and- transformations and their use for fitting data,” Applied Mathematical Sciences, vol. 2, no. 9–12, pp. 449–462, 2008.