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ISRN Applied Mathematics
Volume 2012 (2012), Article ID 475781, 16 pages
An L-Moment-Based Analog for the Schmeiser-Deutsch Class of Distributions
1Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, 222-J Wham Building, Carbondale, IL 62901-4618, USA
2University of Texas at Arlington, 320B Science Hall, Arlington, TX 76019, USA
Received 28 June 2012; Accepted 7 August 2012
Academic Editors: I. Doltsinis and E. Yee
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.
- B. W. Schmeiser and S. J. Deutsch, “A versatile four parameter family of probability distributions suitable for simulation,” American Institute of Industrial Engineers (AIIE) Transactions, vol. 9, no. 2, pp. 176–182, 1977.
- K. Aardal, Ö Jonsson, and H. Jönsson, “Optimal inventory policies with service-level contraints,” Journal of the Operations Research Society, vol. 40, no. 1, pp. 65–73, 1989.
- O. Tang and R. W. Grubbström, “On using higher-order moments for stochastic inventory systems,” International Journal of Production Economics, vol. 104, no. 2, pp. 454–461, 2006.
- A. Akcay and S. Tayur, “Improved inventory targets in the presence of limited historical demand data,” Manufacturing and Service Operations Management (M&SOM), vol. 13, no. 3, pp. 297–309, 2011.
- J. F. Kottas and H. Lau, “A realistic approach for modeling stochastic lead time distributions,” American Institute of Industrial Engineers (AIIE) Transactions, vol. 11, no. 1, pp. 54–60, 1979.
- J. F. Kottas and H. S. Lau, “Inventory control with general demand and lead time distributions,” International Journal of Systems Science, vol. 10, no. 5, pp. 485–492, 1979.
- J. F. Kottas and H. S. Lau, “The use of versatile distribution families in some stochastic inventory calculations,” Journal of the Operations Research Society, vol. 31, no. 5, pp. 393–403, 1980.
- H. Lau and G. E. Martin, “The effects of skewness and kurtosis of processing times in unpaced lines,” International Journal of Production Research, vol. 25, no. 10, pp. 1483–1492, 1987.
- G. E. Martin, “Predictive formulae for unpaced line efficiency,” International Journal of Production Research, vol. 31, no. 8, pp. 1981–1990, 1993.
- H. Lau, “The production rate of a two-stage system with stochastic processing times,” International Journal of Production Research, vol. 24, no. 2, pp. 401–412, 1986.
- H. Lau, A. Lau, and C. Ho, “Improved moment-estimation formulas using more than three subjective fractiles,” Management Science, vol. 44, no. 3, pp. 346–351, 1998.
- C. Somarajan and H.-S. Lau, “Stochastic activity networks: a four-parameter approach for completion times,” International Journal of Systems Science, vol. 25, no. 10, pp. 1607–1619, 1994.
- H. S. Lau, “The newsboy problem under alternative optimization objectives,” Journal of the Operations Research Society, vol. 31, no. 6, pp. 525–535, 1980.
- T. C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2010.
- J. R. M. Hosking, “-moments: analysis and estimation of distributions using linear combinations of order statistics,” Journal of the Royal Statistical Society, 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. 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, “Simulating non-normal distributions with specified L-moments and L-correlations,” Statistica Neerlandica. In press.
- 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.
- T. C. Headrick, “A characterization of power method transformations through -moments,” Journal of Probability and Statistics, vol. 2011, Article ID 497463, 22 pages, 2011.
- TIBCO Software, TIBCO Spotfire S+ 8.1 for Windows, 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.