The power method transformation: its probability density function, distribution function, and its further use for fitting data

Abstract

The power method polynomial transformation is a popular algorithm used for simulating non-normal distributions because of its simplicity and ease of execution. The primary limitations of the power method transformation are that its probability density function (pdf) and cumulative distribution function (cdf) are unknown. In view of this, the power method's pdf and cdf are derived in general form. More specific properties are also derived for determining if a given transformation will also have an associated pdf in the context of polynomials of order three and five. Numerical examples and para-metric plots of power method densities are provided to confirm and demonstrate the methodology. It is also shown how the power method transformation can be applied in the context of parameter estimation and distribution fitting using data from the National Institute on Alcohol Abuse and Alcoholism study Project MATCH.

Keywords:

• Cumulants
• Distribution fitting
• Moments
• Monte Carlo
• Non-normality
• Simulation