Headrick Statistical Simulation

Power Method Polynomials and Other Transformations
Erscheinungsjahr 2010
ISBN: 978-1-4200-6491-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 174 Seiten

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, before demonstrating this method through examples of standard normal, logistic, and uniform power method pdfs. It also discusses methods for improving the performance of a simulation based on power method polynomials. The book then develops simulation procedures for systems of linear statistical models, intraclass correlation coefficients, and correlated continuous variates and ranks. Numerical examples and results from Monte Carlo simulations illustrate these procedures. The final chapter describes how the g-and-h and generalized lambda distribution (GLD) transformations are special applications of the more general multivariate nonnormal data generation approach. Throughout the text, the author employs Mathematica® in a range of procedures and offers the source code for download online.

Written by a longtime researcher of the power method, this book explains how to simulate nonnormal distributions via easy-to-use power method polynomials. By using the methodology and techniques developed in the text, readers can evaluate different transformations in terms of comparing percentiles, measures of central tendency, goodness-of-fit tests, and more.

Zielgruppe

Researchers and graduate students in statistics; quantitative researchers in the medical, biological, and social sciences.

Autoren/Hrsg.

Headrick, Todd C.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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

Über Autor(innen)

Todd C. Headrick is an associate professor and coordinator of the Educational Statistics & Measurement program at Southern Illinois University Carbondale.