E-Book, Englisch, 438 Seiten
Karian / Dudewicz Fitting Statistical Distributions
Erscheinungsjahr 2010
ISBN: 978-1-4200-3804-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
The Generalized Lambda Distribution and Generalized Bootstrap Methods
E-Book, Englisch, 438 Seiten
ISBN: 978-1-4200-3804-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Zielgruppe
Professionals in science, statistics, engineering, and allied disciplines; Faculty and students in graduate level programs in Operations Research, Statistics, or Industrial Engineering
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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
