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Full-Text Articles in Physical Sciences and Mathematics
Statistical Simulation: Power Method Polynomials And Other Transformations, Todd C. Headrick
Statistical Simulation: Power Method Polynomials And Other Transformations, Todd C. Headrick
Todd Christopher Headrick
Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data generation, Statistical Simulation: Power Method Polynomials and Other Transformations presents techniques for conducting a Monte Carlo simulation study. It shows how to use power method polynomials for simulating univariate and multivariate nonnormal distributions with specified cumulants and correlation matrices. The book first explores the methodology underlying the power method, …
Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky
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 …