doi:10.1155/2011/497463 Research Article A Characterization of Power Method Transformations through L-Moments

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Power method polynomial transformations are commonly used for simulating continuous non-normal distributions with specified moments. However, conventional moment-based estimators can a be substantially biased, b have high variance, or c be influenced by outliers. In view of these concerns, a characterization of power method transformations by L-moments is introduced. Specifically, systems of equations are derived for determining coefficients for specified L-moment ratios, which are associated with standard normal and standard logistic-based polynomials of order five and three. Boundaries for L-moment ratios are also derived, and closed-formed formulae are provided for determining if a power method distribution has a valid probability density function. It is demonstrated that L-moment estimators are nearly unbiased and have relativel