Weighted simplex procedures for determining boundary points and constants for the univariate and multivariate power methods

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 erogenous value of skew; there is associated lower bound of kurtosis. Previous approximations of the boundary for the power methods cue either incorrect or inadequate. Data sets from eduction and psychology can be found to lie within, near, or outside the boundary of the pourer methods. In view of this, we derived necessary and sufficient conditions using the L grange multiplier method to determine the boundary of the power methods. The conditions fur locating arid classifying modes for distributions on the bound 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.