Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, 1st Edition (Hardback) book cover

Fitting Statistical Distributions

The Generalized Lambda Distribution and Generalized Bootstrap Methods, 1st Edition

By Zaven A. Karian, Edward J. Dudewicz

Chapman and Hall/CRC

438 pages

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pub: 2000-05-24
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Description

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.

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

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

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General