 Weighted Simplex Procedures for Determining Boundary Points and Constants for the Univariate and Multivariate Power MethodsTodd C. Headrick and Shlomo S. Sawilowsky Journal of Educational and Behavioral Statistics, 2000, vol. 25, issue 4, 417-436 Abstract: The power methods are simple and efficient algorithms used to generate either univariate or multivariate nonnormal 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 tile boundary of the power methods. In view of this, we derived necessary and sufficient conditions using the Lagrange multiplier method to determine the boundary of the power methods. The conditions for locating and classifying modes for distributions on the boundary were also derived. Self-contained interactive Fortran programs using a Weighted Simplex Procedure were employed to generate tabled values of minimum kurtosis for a given value of skew and power constants for various (non)normal distributions. Keywords: power method; weighted simplex procedure; skew; kurtosis; nonnormal distributions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:25:y:2000:i:4:p:417-436 DOI: 10.3102/10769986025004417 Access Statistics for this article More articles in Journal of Educational and Behavioral Statistics |
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