Physical Sciences and Mathematics Commons^™

Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky

Todd Christopher Headrick

The power methods are simple and efficient algorithms used to generate either univariate or multivariate non-normal distributions with specified values of (marginal) mean, standard deviation, skew, and kurtosis. The power methods are bounded as are other transformation techniques. Given an exogenous value of skew, there is an associated lower bound of kurtosis. Previous approximations of the boundary for the power methods are either incorrect or inadequate. Data sets from education and psychology can be found to lie within, near or outside the boundary of the power methods. In view of this, we derived necessary and sufficient conditions using the Lagrange …