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Full-Text Articles in Physical Sciences and Mathematics
Simulating Multivariate G-And-H Distributions, Rhonda K. Kowalchuk, Todd C. Headrick
Simulating Multivariate G-And-H Distributions, Rhonda K. Kowalchuk, Todd C. Headrick
Todd Christopher Headrick
The Tukey family of g-and-h distributions is often used to model univariate real-world data. There is a paucity of research demonstrating appropriate multivariate data generation using the g-and-h family of distributions with specified correlations. Therefore, the methodology and algorithms are presented to extend the g-and-h family from univariate to multivariate data generation. An example is provided along with a Monte Carlo simulation demonstrating the methodology. In addition, algorithms written in Mathematica 7.0 are available from the authors for implementing the procedure.
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, …