Handbook of Fitting Statistical Distributions with R: 1st Edition (Hardback) book cover

Handbook of Fitting Statistical Distributions with R

1st Edition

By Zaven A. Karian, Edward J. Dudewicz

Chapman and Hall/CRC

1,718 pages | 532 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781584887119
pub: 2010-10-01

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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.


"… 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

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.

About the Authors

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.

Subject Categories

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