Strengthened by examples taken from the scientific literature, this handbook provides statisticians and researchers across the physical and social sciences with cutting-edge methods for fitting continuous probability distributions. It presents families with wide-ranging applicability, including Johnson's system, kappa distribution, and generalized lambda distribution.
By providing the necessary R programs, the book enables practitioners to implement the techniques using R computer code. To cover distribution method combinations not included in the book's extensive tables, the authors delve into the application of computational algorithms and attendant approximation errors.
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 L# 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
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. Edward J. Dudewicz is a professor of mathematics at Syracuse University in New York.
