With the development of new fitting methods, their increased use in applications, and improved computer languages, the fitting of statistical distributions to data has come a long way since the introduction of the generalized lambda distribution (GLD) in 1969. Handbook of Fitting Statistical Distributions with R presents the latest and best methods, algorithms, and computations for fitting distributions to data. It also provides in-depth coverage of cutting-edge applications.
The book begins with commentary by three GLD pioneers: John S. Ramberg, Bruce Schmeiser, and Pandu R. Tadikamalla. These leaders of the field give their perspectives on the development of the GLD. The book then covers GLD methodology and Johnson, kappa, and response modeling methodology fitting systems. It also describes recent additions to GLD and generalized bootstrap methods as well as a new approach to goodness-of-fit assessment. The final group of chapters explores real-world applications in agriculture, reliability estimation, hurricanes/typhoons/cyclones, hail storms, water systems, insurance and inventory management, and materials science. The applications in these chapters complement others in the book that deal with competitive bidding, medicine, biology, meteorology, bioassays, economics, quality management, engineering, control, and planning.
New results in the field have generated a rich array of methods for practitioners. Making sense of this extensive growth, this comprehensive and authoritative handbook improves your understanding of the methodology and applications of fitting statistical distributions. The accompanying CD-ROM includes the R programs used for many of the computations.
Table of Contents
Fitting Statistical Distributions: An Overview
The Generalized Lambda Distribution
The Generalized Lambda Family of Distributions
Fitting Distributions and Data with the GLD via the Method of Moments
The Extended GLD System, the EGLD: Fitting by the Method of Moments
A Percentile-Based Approach to Fitting Distributions and Data with the GLD
Fitting Distributions and Data with the GLD through L-Moments
Fitting a GLD Using a Percentile-KS (P-KS) Adequacy Criterion
Fitting Mixture Distributions Using a Mixture of GLDs with Computer Code
GLD–2: The Bivariate GLD
Fitting the GLD with Location and Scale-Free Shape Functionals
Statistical Design of Experiments: A Short Review
Quantile Distribution Methods
Statistical Modeling Based on Quantile Distribution Functions
Distribution Fitting with the Quantile Function of Response Modeling Methodology (RMM)
Fitting GLDs and Mixture of GLDs to Data Using Quantile Matching Method
Fitting GLD to Data Using GLDEX 1.0.4 in R
Other Families of Distributions
Fitting Distributions and Data with the Johnson System via the Method of Moments
Fitting Distributions and Data with the Kappa Distribution through L-Moments and Percentiles
Weighted Distributional Lα Estimates
A Multivariate Gamma Distribution for Linearly Related Proportional Outcomes
The Generalized Bootstrap and Monte Carlo Methods
The Generalized Bootstrap (GB) and Monte Carlo (MC) Methods
The GB: A New Fitting Strategy and Simulation Study Showing Advantage over Bootstrap Percentile Methods
GB Confidence Intervals for High Quantiles
Assessment of the Quality of Fits
Goodness-of-Fit Criteria Based on Observations Quantized by Hypothetical and Empirical Percentiles
Evidential Support Continuum (ESC): A New Approach to Goodness-of-Fit Assessment, which Addresses Conceptual and Practical Challenges
Estimation of Sampling Distributions of the Overlapping Coefficient and Other Similarity Measures
Fitting Statistical Distribution Functions to Small Datasets
Mixed Truncated Random Variable Fitting with the GLD, and Applications in Insurance and Inventory Management
Distributional Modeling of Pipeline Leakage Repair Costs for a Water Utility Company
Use of the GLD in Materials Science, with Examples in Fatigue Lifetime, Fracture Mechanics, Polycrystalline Calculations, and Pitting Corrosion
Fitting Statistical Distributions to Data in Hurricane Modeling
A Rainfall-Based Model for Predicting the Regional Incidence of Wheat Seed Infection by Stagonospora nodorum in New York
Reliability Estimation Using Univariate Dimension Reduction and Extended GLD
Statistical Analyses of Environmental Pressure Surrounding Atlantic Tropical Cyclones
Simulating Hail Storms Using Simultaneous Efficient Random Number Generators
Programs and Their Documentation
Table B–1 for GLD Fits: Method of Moments
Table C–1 for GBD Fits: Method of Moments
Tables D–1 through D–5 for GLD Fits: Method of Percentiles
Tables E–1 through E–5 for GLD Fits: Method of L-Moments
Table F–1 for Kappa Distribution Fits: Method of L-Moments
Table G–1 for Kappa Distribution Fits: Method of Percentiles
Table H–1 for Johnson System Fits in the SU Region: Method of Moments
Table I–1 for Johnson System Fits in the SB Region: Method of Moments
Table J–1 for p-Values Associated with Kolmogorov–Smirnov Statistics
Table K–1 Normal Distribution Percentiles
References appear at the end of each chapter.
Zaven A. Karian holds the Benjamin Barney Chair of Mathematics and is a professor of mathematics and computer science at Denison University in Granville, Ohio. For over thirty-five years, Dr. Karian has been active as an instructor, researcher, and consultant in mathematics, computer science, statistics, and simulation. He has taught many workshops and short courses at various educational institutions, conferences, and professional societies.
Edward J. Dudewicz is a professor of mathematics at Syracuse University in New York. With more than four decades of experience, Dr. Dudewicz is internationally recognized for his solution of the heteroscedastic selection problem, his work on fitting statistical distributions, his development of the multivariate heteroscedastic method, and his solution of the Behrens–Fisher problem.
"... this is an enormously rich and useful handbook representing well the state of art in this area. ... This handbook should be available in any institutional library, and it will be more than useful to both theorists and applied scientists."
—Zentralblatt MATH 1282
"Zaven Karian and Edward Dudewicz, major authorities on the GLD, along with numerous colleagues have authored the most comprehensive reference on the theoretical and applied aspects of the GLD in conjunction with numerous ancillary topics. The Handbook is an exciting benchmark in the four-decade history of the GLD and outstanding anchor for state-of-the-practice. … Is the book recommended? Yes. The Handbook is a milestone on the GLD that should be embraced and have residence on the shelves of many practitioners, including myself. The typeset source code and included CD-ROM of software are valuable. The Handbook provides extensive real-world examples by the authors and numerous contributors pertaining to distributional analysis requiring the flexibility of the GLD. Therefore, the Handbook is also recommended for advanced data analysts."
—The American Statistician, May 2014
"… reading through this book is certainly an enlightening experience—many different aspects of GLD modeling are shown and motivated (including the interesting potential for GLD mixture use in chromatographic spectra modelling). Interesting and idea-rich presentations of much more general approaches appear in various chapters …"
—ISCB News, June 2012