1st Edition
Statistical Simulation Power Method Polynomials and Other Transformations
Introduction
The Power Method Transformation
Univariate Theory
Third-Order Systems
Fifth-Order Systems
Mathematica® Functions
Limitations
Multivariate Theory
Using the Power Method Transformation
Introduction
Examples of Third- and Fifth-Order Polynomials
Remediation Techniques
Monte Carlo Simulation
Some Further Considerations
Simulating More Elaborate Correlation Structures
Introduction
Simulating Systems of Linear Statistical Models
Methodology
Numerical Example and Monte Carlo Simulation
Some Additional Comments
Simulating Intraclass Correlation Coefficients
Methodology
Numerical Example and Monte Carlo Simulation
Simulating Correlated Continuous Variates and Ranks
Methodology
Numerical Example and Monte Carlo Simulation
Some Additional Comments
Other Transformations: The g-and-h and GLD Families of Distributions
Introduction
The g-and-h Family
The Generalized Lambda Distributions (GLDs)
Numerical Examples
Multivariate Data Generation
References
Index
Biography
Todd C. Headrick is an associate professor and coordinator of the Educational Statistics & Measurement program at Southern Illinois University Carbondale.
Headrick’s book is a valuable addition to the simulation world in the sense that it is the first systematic book on power method polynomials … this book has potential to be one of the key sources for researchers who are involved in random number generation and Monte Carlo studies. … it can serve and seems to be designed as a supplemental text in graduate level simulation- and computation-oriented courses. … Mathematica functions are provided throughout the book, which is a nice feature … Headrick’s book is a fairly major contribution to the literature … . I would highly recommend this book to anyone who deals with random number generation and more generally with Monte Carlo simulation and statistical computing.
—Journal of Statistical Software, Vol. 43, September 2011This interesting monograph concerns the use of power method polynomials in the context of simulating univariate and multivariate nonnormal distributions with given cumulant and correlation structure. Its strength is in the fact that the power method, g-and-h transformations and GLD transformations are capable of simulation multivariate nonnormal continuous distributions specified by its cumulants and correlation matrices. … —Zentralblatt MATH 1187
