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A Doubling Technique for the Power Method Transformations
Applied Mathematical Sciences (2012)
  • Mohan D. Pant, University of Texas at Arlington
  • Todd C. Headrick, Southern Illinois University Carbondale
Abstract
Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with specified values of L-skew, L-kurtosis, and L-correlation. Evaluation of the proposed doubling technique indicates that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moments in terms of relative bias and relative efficiency when extreme non-normal distributions are of concern.
Keywords
  • Doubling Technique,
  • Monte Carlo Simulation,
  • Skew,
  • Kurtosis,
  • L-Skew,
  • L-Kurtosis
Publication Date
Fall October 5, 2012
Citation Information
Mohan D. Pant and Todd C. Headrick. "A Doubling Technique for the Power Method Transformations" Applied Mathematical Sciences Vol. 6 Iss. 130 (2012)
Available at: http://works.bepress.com/mohan_pant/6/