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Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods [Kõva köide]

(Denison University, Granville, Ohio, USA), (Syracuse University, Syracuse, New York, USA)
  • Formaat: Hardback, 456 pages, kõrgus x laius: 234x156 mm, kaal: 1000 g, 88 Tables, black and white
  • Ilmumisaeg: 24-May-2000
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584880694
  • ISBN-13: 9781584880691
Teised raamatud teemal:
  • Formaat: Hardback, 456 pages, kõrgus x laius: 234x156 mm, kaal: 1000 g, 88 Tables, black and white
  • Ilmumisaeg: 24-May-2000
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584880694
  • ISBN-13: 9781584880691
Teised raamatud teemal:
Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?

Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do not exist.

Regardless of your specific field-physical science, social science, or statistics, practitioner or theorist-Fitting Statistical Distributions is required reading. It includes wide-ranging applications illustrating the methods in practice and offers proofs of key results for those involved in theoretical development. Without it, you may be using obsolete methods, wasting time, and risking incorrect results.
Preface v
About the Authors 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)
Example: Cadmium in Horse Kidneys
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)
Example: Cadmium in Horse Kidneys
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


Karian, Zaven A.; Dudewicz, Edward J.