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Tables of Contents for Fitting Statistical Distributions
Chapter/Section Title
Page #
Page Count
Preface
v

vii

Dedication
xi

The Generalized Lambda Family of Distributions
1
40
History and Background
3
6
Definition of the Generalized Lambda Distributions
9
2
The Parameter Space of the GLD
11
10
Shapes of the GLD Density Functions
21
16
GLD Random Variate Generation
37
4
Problems for Chapter 1
38
3
Fitting Distributions and Data with the GLD via the Method of Moments
41
72
The Moments of the GLD Distribution
43
4
The (α2 3, α4)-Space Covered by the GLD Family
47
6
Fitting the GLD Through the Method of Moments
53
13
Fitting through Direct Computation
54
9
Fitting by the Use of Tables
63
1
Limitations of the Method of Moments
64
2
GLD Approximations of Some Well-Known Distributions
66
26
The Normal Distribution
67
1
The Uniform Distribution
68
2
The Student's t Distribution
70
1
The Exponential Distribution
71
2
The Chi-Square Distribution
73
2
The Gamma Distribution
75
1
The Weibull Distribution
76
2
The Lognormal Distribution
78
1
The Beta Distribution
79
2
The Inverse Gaussian Distribution
81
1
The Logistic Distribution
82
2
The Largest Extreme Value Distribution
84
1
The Extreme Value Distribution
84
2
The Double Exponential Distribution
86
1
The F-Distribution
87
2
The Pareto Distribution
89
1
Summary of Distributions and their GLD fits
90
2
Examples: GLD Fits of Data, Method of Moments
92
12
Assessment of Goodness-of-Fit
93
3
96
2
Example: Brain (Left Thalamus) MRI Scan Data
98
1
Example: Human Twin Data for Quantifying Genetic (vs. Environmental) Variance
99
3
Example: Rainfall Distributions
102
2
Moment-Based GLD Fit to Data from a Histogram
104
3
The GLD and Design of Experiments
107
6
Problems for Chapter 2
111
2
The Extended GLD System, the EGLD: Fitting by the Method of Moments
113
40
The Beta Distribution and its Moments
113
6
The Generalized Beta Distribution and its Moments
119
4
Estimation of GBD (β1, β2, β3, β4) Parameters
123
6
GBD Approximations of Some Well-Known Distributions
129
10
The Normal Distribution
130
1
The Uniform Distribution
131
1
The Student's t Distribution
131
1
The Exponential Distribution
132
1
The Chi-Square Distribution
133
1
The Gamma Distribution
134
1
The Weibull Distribution
134
2
The Lognormal Distribution
136
1
The Beta Distribution
137
1
The Inverse Gaussian Distribution
138
1
The Logistic Distribution
138
1
The Largest Extreme Value Distribution
138
1
The Extreme Value Distribution
138
1
The Double Exponential Distribution
139
1
The F-Distribution
139
1
The Pareto Distribution
139
1
Examples: GBD Fits of Data, Method of Moments
139
11
Example: Fitting a GBD to Simulated Data from GBD (3, 5, 0, -0.5)
140
1
Example: Fitting a GBD to Data Simulated from GBD (2, 7, 1, 4)
141
2
143
1
Example: Rainfall Data of Section 2.5.5
144
2
Example: Tree Stand Heights and Diameters in Forestry
146
4
EGLD Random Variate Generation
150
3
Problems for Chapter 3
151
2
A Percentile-Based Approach to Fitting Distributions and Data with the GLD
153
64
The Use of Percentiles
154
3
The (ρ3, ρ4)-space of GLD (λ1, λ2, λ3, λ4)
157
6
Estimation of GLD Parameters Through a Method of Percentiles
163
6
GLD Approximations of Some Well-Known Distributions
169
27
The Normal Distribution
169
2
The Uniform Distribution
171
1
The Student's t Distribution
171
3
The Exponential Distribution
174
2
The Chi-Square Distribution
176
1
The Gamma Distribution
177
2
The Weibull Distribution
179
1
The Lognormal Distribution
180
3
The Beta Distribution
183
1
The Inverse Gaussian Distribution
184
2
The Logistic Distribution
186
1
The Largest Extreme Value Distribution
187
2
The Extreme Value Distribution
189
1
The Double Exponential Distribution
189
2
The F-Distribution
191
1
The Pareto Distribution
192
2
Summary of Distribution Approximations
194
2
Comparison of the Moment and Percentile Methods
196
7
Examples: GLD Fits of Data via the Method of Percentiles
203
9
Example: Data from the Cauchy Distribution
204
2
Data on Radiation in Soil Samples
206
2
Data on Velocities within Galaxies
208
1
Rainfall Data of Sections 2.5.5 and 3.5.4
208
4
Percentile-Based GLD Fit of Data from a Histogram
212
5
Problems for Chapter 4
214
3
GLD--2: The Bivariate GLD Distribution
217
56
Overview
218
3
Plackett's Method of Bivariate d.f. Construction: The GLD-2
221
10
Fitting the GLD-2 to Well-Known Bivariate Distributions
231
16
The Bivariate Normal (BVN) Distribution
232
6
Gumbel's Bivariate Exponential Type I (BVE)
238
1
Bivariate Cauchy (BVC)
238
6
Kibble's Bivariate Gamma (BVG)
244
3
GLD-2 Fits: Distributions with Non-Identical Marginals
247
5
Bivariate Gamma BVG with Non-Identical Marginals
247
1
Bivariate with Normal and Cauchy Marginals
247
2
Bivariate with Gamma and ``Backwards Gamma'' Marginals
249
3
Fitting GLD-2 to Datasets
252
13
Algorithm for Fitting the GLD-2 to Data
252
8
Example: Human Twin Data of Section 2.5.4
260
2
Example: The Rainfall Distributions of Section 2.5.5
262
2
Example: The Tree Stand Data of Section 3.5.5
264
1
GLD-2 Random Variate generation
265
4
Conclusions and Research Problems Regarding GLD-2
269
4
Problems for Chapter 5
271
2
The Generalized Bootstrap (GB) and Monte Carlo (MC) Methods
273
12
The Generalized Bootstrap (GB) Method
274
8
Comparisons of the GB and BM Methods
282
3
Problems for Chapter 6
282
3
Appendices
285
132
A Programs for Fitting the GLD, GBD, and GLD-2
285
24
A.1 General Utility Programs
287
4
A.2 GLD Parameter Estimation: Method of Moments
291
3
A.3 GBD Parameter Estimation: Method of Moments
294
2
A.4 GLD Parameter Estimation: Method of Percentiles
296
2
A.5 Programs for GLD-2 Fitting
298
11
B Table B-1 for GLD Fits: Method of Moments
309
22
C Table C-1 for GBD Fits: Method of Moments
331
26
D Tables for GLD Fits: Method of Percentiles
357
56
E The Normal Distribution
413
4
References and Author Index
417
12
Subject Index
429