Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods
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Summary
Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?
Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do not exist.
Regardless of your specific field-physical science, social science, or statistics, practitioner or theorist-Fitting Statistical Distributions is required reading. It includes wide-ranging applications illustrating the methods in practice and offers proofs of key results for those involved in theoretical development. Without it, you may be using obsolete methods, wasting time, and risking incorrect results.
Table of Contents
THE GENERALIZED LAMBDA FAMILY OF DISTRIBUTIONS
History and Background
Definition of the Generalized Lambda Distributions
The Parameter Space of the GLD
Shape of the GLD Density Functions
GLD Random Variate Generation
FITTING DISTRIBUTIONS AND DATA WITH THE GLD VIA THE METHOD OF MOMENTS
The Moments of the GLD Distribution
The (a23, a4)-Space Covered by the GLD Family
Fitting the GLD through the Method of Moments
GLD Approximation of some Well Known Distributions
Examples: GLD Fits of Data, Method of Moments
Moment-Based GLD Fit to Data from a Histogram
The GLD and Design of Experiments
THE EXTENDED GLD SYSTEM, THE EGLD: FITTING BY THE METHOD OF MOMENTS
The Beta Distribution and its Moments
The Generalized Beta Distribution and its Moments
Estimation of GBD (b1, b2, b3, b4) Parameters
GBD Approximation of some Well-Known Distributions
Examples: GBD Fits of Data, Method of Moments
EGLD Random Variate Generation
A PERCENTILE-BASED APPROACH TO FITTING DISTRIBUTIONS AND DATA WITH THE GLD
The Use of Percentiles
The (r3, r4-Space of GLD (l1, l2, l3, l4)
Estimation of GLD Parameters through a Method of Percentiles
GLD Approximations of some Well-Known Distributions
Comparison of the Moment and Percentile Methods
Examples: GLD Fits of Data via the Method of Percentiles
Percentile-Based GLD Fit of Data from a Histogram
GLD-2: THE BIVARIATE GLD DISTRIBUTION
Overview
Plackett's Method of Bivariate d.f. Construction: the GLD-2
Fitting the GLD-2 to Well-Known Bivariate Distributions
GLD-2 Fits: Distributions with Non-Identical Marginals
Fitting GLD-2 to Datasets
GLD-2 Random Variate Generation
THE GENERALIZED BOOTSTRAP (GB) AND MONTE CARLO (MC) METHODS
The Generalized Bootstrap Method
Comparison of the GB and BM Methods
APPENDICES
Programs for Fitting the GLD, GBD, and GLD-2
Tables for GLD Fits: Method of Moments
Tables for GBD Fits: Method of Moments
Tables for GLD Fits: method of Percentiles
The Normal Distribution
Editorial Reviews
"The generalized lambda family of distributions is a very broad family of continuous univariate probability distributions. The authors have been at the forefront in investigating this distribution…they thoroughly explore the relationship of the generalized lambda family of distributions to many commonly used families of distributions…provide a thorough exploration of the generalized lambda family of distributions and its use in the fitting of data. Practitioners who wish to fit data with a generalized lambda distribution will find this book useful. Numerous examples with actual datasets illustrate the utility of the techniques…In summary, the authors have presented a complete exploration of the use of a particular family of distributions in fitting data."
- Thomas E. Wehrly, Texas A & M University, Technometrics, May 2002
"In this outstanding treatise the GLD is explored in depth. The writing is clear and the mathematical analyses are easy to follow."
-Telegraphic Reviews
"This book is clearly written, and provides an excellent summary of what is currently known about the GLD, and indeed the authors have made major contributions to this body of knowledge in the last few years…"
--M. S. Ridout, Biometrics, June 2001
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| 2885.zip | All Windows Version | September 10, 2001 |
