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Simulating Uniform- and Triangular- Based Double Power Method Distributions

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  • Mohan D. Pant
  • Todd C. Headrick

Abstract

Power method (PM) polynomials have been used for simulating non-normal distributions in a variety of settings such as toxicology research, price risk, business-cycle features, microarray analysis, computer adaptive testing, and structural equation modeling. A majority of these applications are based on the method of matching product moments (e.g., skew and kurtosis). However, estimators of skew and kurtosis can be (a) substantially biased, (b) highly dispersed, or (c) influenced by outliers. To address this limitation, two families of double-uniform-PM and double-triangular-PM distributions are characterized through the method of ๐ฟ-moments using a doubling technique. The ๐ฟ-moment based procedure is contrasted with the method of product moments in the contexts of fitting real data and estimation of parameters. A methodology for simulating correlated double-uniform-PM and double-triangular-PM distributions with specified values of ๐ฟ-skew, ๐ฟ-kurtosis, and ๐ฟ-correlation is also demonstrated. Monte Carlo simulation results indicate that the L-moment-based estimators ofร‚ ๐ฟ-skew, ๐ฟ-kurtosis, and ๐ฟ-correlation are superior to their product moment-based counterparts.Mathematics Subject Classification: 60E05; 62G30; 62H12; 62H20; 65C05; 65C10; 65C60; 78M05Keywords: Product moments; Pearson correlation; ๐ฟ-moments; ๐ฟ-correlation

Suggested Citation

  • Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.
  • Handle: RePEc:spt:stecon:v:6:y:2017:i:1:f:6_1_1
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    References listed on IDEAS

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    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    4. Hess, Gregory D & Iwata, Shigeru, 1997. "Measuring and Comparing Business-Cycle Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 432-444, October.
    5. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 251-251, June.
    6. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 25-35, March.
    7. Steyn, H. S., 1993. "On the Problem of More Than One Kurtosis Parameter in Multivariate Analysis," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 1-22, January.
    8. Beasley, T. Mark & Zumbo, Bruno D., 2003. "Comparison of aligned Friedman rank and parametric methods for testing interactions in split-plot designs," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 569-593, April.
    9. Todd C. Headrick & Mohan D. Pant, 2012. "Simulating non-normal distributions with specified L-moments and L-correlations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 422-441, November.
    10. Demirtas, Hakan & Hedeker, Donald, 2011. "A Practical Way for Computing Approximate Lower and Upper Correlation Bounds," The American Statistician, American Statistical Association, vol. 65(2), pages 104-109.
    11. Affleck-Graves, John & McDonald, Bill, 1989. " Nonnormalities and Tests of Asset Pricing Theories," Journal of Finance, American Finance Association, vol. 44(4), pages 889-908, September.
    12. Headrick, Todd C. & Rotou, Ourania, 2001. "An investigation of the rank transformation in multiple regression," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 203-215, December.
    13. Headrick, Todd C., 2002. "Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 685-711, October.
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