Books  Data Analysis & Modelling  Data Analysis & Statistics 

Handbook of Fitting Statistical Distributions with R

By: Zaven A Karian and Edward J Dudewicz

1672 pages, 532 figs, 142 tabs

Chapman & Hall (CRC Press)

Hardback | Oct 2010 | #188004 | ISBN-13: 9781584887119
Availability: Usually dispatched within 6 days Details
NHBS Price: £95.00 $121/€113 approx

About this book

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.


Contents

Overview

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

Applications

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

Appendices

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

Index

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Biography

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.

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