A Characterization of the Power Method Transformation through the Method of Percentiles

• Activity Number: 82
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jennifer Koran*+ and Todd C. Headrick and Tzu Chun Kuo
• Companies: Southern Illinois University Carbondale and Southern Illinois University Carbondale and Southern Illinois University Carbondale
• Keywords: Monte Carlo ; power method ; pseudo-random numbers ; simulation ; method of percentiles

Abstract

This paper derives a standard normal based power method polynomial transformation for Monte Carlo simulation studies, approximating distributions, and fitting distributions to data based on the method of percentiles. The proposed method is used primarily when (i) conventional estimators such as skew and kurtosis are unknown or (ii) data are unavailable but percentiles are known (e.g., standardized test score reports). The proposed transformation also has the advantage that solutions to polynomial coefficients are available in simple closed form and thus obviates numerical equation solving. The Monte Carlo results presented in this study indicate that the estimators based on the method of percentiles are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias.