Fitting Statistical Distributions

Fitting Statistical Distributions : The Generalized Lambda Distribution and Generalized Bootstrap Methods

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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 more

Product details

  • Hardback | 438 pages
  • 163.6 x 241.6 x 30mm | 895.77g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2003.
  • 88 black & white tables
  • 1584880694
  • 9781584880691

Review quote

"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 distributionthey thoroughly explore the relationship of the generalized lambda family of distributions to many commonly used families of distributionsprovide 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 techniquesIn 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 2001show more

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 Distributionshow more

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