A Characterization of Power Method Transformations Through the Method of Percentiles

• In Event: 53.067 - Statistical Research in the Contexts of Parametric Assumption Violations, Simulation, Structural Equation Modeling, and Ordinal or Nominal Data Analyses

Abstract

This paper derives closed-form solutions for the 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 sixth-ordered 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 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.

Authors

• Tzu Chun Kuo, American Institutes for Research

• Todd Christopher Headrick, Southern Illinois University - Carbondale