Handbook of Fitting Statistical Distributions with R

Handbook of Fitting Statistical Distributions with R

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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.show more

Product details

  • Electronic book text | 1718 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 2000+; 142 Tables, black and white; 532 Illustrations, black and white
  • 1584887125
  • 9781584887126

Table of contents

Overview Fitting Statistical Distributions: An Overview The Generalized Lambda Distribution The Generalized Lambda Family of DistributionsFitting Distributions and Data with the GLD via the Method of MomentsThe Extended GLD System, the EGLD: Fitting by the Method of MomentsA Percentile-Based Approach to Fitting Distributions and Data with the GLDFitting Distributions and Data with the GLD through L-MomentsFitting a GLD Using a Percentile-KS (P-KS) Adequacy CriterionFitting Mixture Distributions Using a Mixture of GLDs with Computer CodeGLD-2: The Bivariate GLD Fitting the GLD with Location and Scale-Free Shape FunctionalsStatistical Design of Experiments: A Short Review Quantile Distribution Methods Statistical Modeling Based on Quantile Distribution FunctionsDistribution Fitting with the Quantile Function of Response Modeling Methodology (RMM)Fitting GLDs and Mixture of GLDs to Data Using Quantile Matching MethodFitting 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 MomentsFitting Distributions and Data with the Kappa Distribution through L-Moments and PercentilesWeighted Distributional Lα EstimatesA Multivariate Gamma Distribution for Linearly Related Proportional Outcomes The Generalized Bootstrap and Monte Carlo Methods The Generalized Bootstrap (GB) and Monte Carlo (MC) MethodsThe GB: A New Fitting Strategy and Simulation Study Showing Advantage over Bootstrap Percentile MethodsGB Confidence Intervals for High Quantiles Assessment of the Quality of Fits Goodness-of-Fit Criteria Based on Observations Quantized by Hypothetical and Empirical PercentilesEvidential Support Continuum (ESC): A New Approach to Goodness-of-Fit Assessment, which Addresses Conceptual and Practical ChallengesEstimation of Sampling Distributions of the Overlapping Coefficient and Other Similarity Measures ApplicationsFitting Statistical Distribution Functions to Small DatasetsMixed Truncated Random Variable Fitting with the GLD, and Applications in Insurance and Inventory ManagementDistributional Modeling of Pipeline Leakage Repair Costs for a Water Utility CompanyUse of the GLD in Materials Science, with Examples in Fatigue Lifetime, Fracture Mechanics, Polycrystalline Calculations, and Pitting CorrosionFitting Statistical Distributions to Data in Hurricane ModelingA Rainfall-Based Model for Predicting the Regional Incidence of Wheat Seed Infection by Stagonospora nodorum in New YorkReliability Estimation Using Univariate Dimension Reduction and Extended GLDStatistical Analyses of Environmental Pressure Surrounding Atlantic Tropical CyclonesSimulating Hail Storms Using Simultaneous Efficient Random Number Generators AppendicesPrograms and Their DocumentationTable 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 Index References appear at the end of each chapter.show more

About Zaven A. Karian

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.show more

Review quote

"... 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 2012show more