A characterization of power method transformations through the method of percentiles

Abstract

This paper derives closed-form solutions for the fifth-ordered power method polynomial transformation based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew, kurtosis, fifth-and sixthordered functions. The MOP methodology is also extended from univariate to multivariate data generation. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. In addition, the MOP procedure can be applied to distributions where mean and(or) variance do(does) not exist. Simulation results demonstrate that the proposed MOP procedure is superior to the MOM in terms of estimation, relative bias, and relative error.