Statistical Distributions, 3rd Edition

by Merran Evans (Monash Univ., Australia); Nicholas Hastings (Queensland Univ. of Technology, Australia); Brian Peacock (General Motors Technical Center, MI)
Edition: 3rd
Format: Paperback
Pub. Date: 2000-07-01
Publisher(s): Wiley-Interscience
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Summary

From the reviews: "Concise and useful summaries of the salient facts and formulas relating to [various] distributions." -Journal of the American Statistical Association "A worthwhile reference." -Journal of Quality Technology Since the previous edition of this popular guide to the most commonly used statistical distributions was published in 1993, statistical methods have found many new applications in science, medicine, engineering, business/finance, and the social sciences. To keep pace with these developments and to highlight the growing influence of statistical software and data management techniques, this new edition is now thoroughly updated and revised. Through clear, concise, easy-to-follow presentations, the authors discuss the key facts and formulas for 40 major probability distributions, fine-tune all existing material, and continue to offer ready access to vital information gleaned from hard-to-find places across the literature. Highly useful both as an introduction to basic principles and as a quick reference guide, Statistical Distributions, Third Edition: * Presents the 40 distributions in alphabetical order * Provides all key formulas for each distribution * Adds a new chapter on the Empirical Distribution Function * Expands the Weibull Distribution to cover the 3 and 5 parameter versions * Incorporates diagrams and tables illustrating the characteristics of each distribution * Discusses the types of application for which distributions are used * Features references to relevant software packages

Author Biography

MERRAN EVANS, PhD, is Director of Planning and Academic Affairs at Monash University, Victoria, Australia. NICHOLAS HASTINGS, PhD, is Director of the Centre for Asset Management at Queensland University of Technology, Brisbane, Australia. BRIAN PEACOCK, PhD, is Manager of Manufacturing Ergonomics Laboratory, General Motors Technical Center, Warren, Michigan

Table of Contents

Preface xv
Introduction
1(2)
Terms and Symbols
3(14)
Probability, Random Variable, Variate, and Random Number
3(2)
Range, Quantile, Probability Statements and Domain, and Distribution Function
5(3)
Inverse Distribution and Survival Function
8(1)
Probability Density Function and Probability Function
9(2)
Other Associated Functions and Quantities
11(6)
General Variate Relationships
17(14)
Introduction
17(1)
Function of a Variate
17(1)
One-to-One Transformations and Inverses
18(2)
Variate Relationships Under One-to-One Transformation
20(2)
Parameters, Variate, and Function Notation
22(2)
Transformation of Location and Scale
24(1)
Transformation from the Rectangular Variate
25(1)
Many-to-One Transformations
26(3)
Functions of Several Variates
29(2)
Bernoulli Distribution
31(3)
Random Number Generation
32(1)
Curtailed Bernoulli Trial Sequences
32(1)
Urn Sampling Scheme
33(1)
Note
33(1)
Beta Distribution
34(9)
Notes on Beta and Gamma Functions
35(2)
Variate Relationships
37(3)
Parameter Estimation
40(1)
Random Number Generation
41(1)
Inverted Beta Distribution
41(1)
Noncentral Beta Distribution
42(1)
Beta Binomial Distribution
42(1)
Binomial Distribution
43(5)
Variate Relationships
44(2)
Parameter Estimation
46(1)
Random Number Generation
47(1)
Cauchy Distribution
48(4)
Note
49(1)
Variate Relationships
49(1)
Random Number Generation
50(1)
Generalized Form
50(2)
Chi-Squared Distribution
52(6)
Variate Relationships
53(4)
Random Number Generation
57(1)
Chi Distribution
57(1)
Chi-Squared (Noncentral) Distribution
58(4)
Variate Relationships
59(3)
Dirichlet Distribution
62(3)
Variate Relationships
62(1)
Dirichlet Multinomial Distribution
63(2)
Empirical Distribution Function
65(6)
Estimation from Uncensored Data
65(1)
Estimation from Censored Data
66(1)
Parameter Estimation
67(1)
Example
67(2)
Graphical Method for the Modified Order-Numbers
69(1)
Model Accuracy
70(1)
Erlang Distribution
71(3)
Variate Relationships
72(1)
Parameter Estimation
73(1)
Random Number Generation
73(1)
Error Distribution
74(3)
Note
75(1)
Variate Relationships
76(1)
Exponential Distribution
77(5)
Note
79(1)
Variate Relationships
80(1)
Parameter Estimation
81(1)
Random Number Generation
81(1)
Exponential Family
82(3)
Members of the Exponential Family
82(1)
Univariate One-Parameter Exponential Family
82(2)
Estimation
84(1)
Extreme Value (Gumbel) Distribution
85(5)
Note
86(1)
Variate Relationships
86(3)
Parameter Estimation
89(1)
Random Number Generation
89(1)
F (Variance Ratio) or Fisher-Snedecor Distribution
90(5)
Variate Relationships
91(4)
F (Noncentral) Distribution
95(3)
Variate Relationships
96(2)
Gamma Distribution
98(8)
Variate Relationships
99(2)
Parameter Estimation
101(1)
Random Number Generation
102(1)
Inverted Gamma Distribution
103(1)
Normal Gamma Distribution
103(1)
Generalized Gamma Distribution
104(2)
Geometric Distribution
106(3)
Notes
107(1)
Variate Relationships
108(1)
Random Number Generation
108(1)
Hypergeometric Distribution
109(5)
Note
111(1)
Variate Relationships
111(1)
Parameter Estimation
112(1)
Random Number Generation
112(1)
Negative Hypergeometric Distribution
112(1)
Generalized Hypergeometric (Series) Distribution
113(1)
Inverse Gaussian (Wald) Distribution
114(3)
Variate Relationships
115(1)
Parameter Estimation
116(1)
Laplace Distribution
117(4)
Variate Relationships
118(2)
Parameter Estimation
120(1)
Random Number Generation
120(1)
Logarithmic Series Distribution
121(3)
Variate Relationships
122(1)
Parameter Estimation
122(2)
Logistic Distribution
124(5)
Notes
126(1)
Variate Relationships
127(1)
Parameter Estimation
128(1)
Random Number Generation
128(1)
Lognormal Distribution
129(5)
Variate Relationships
130(3)
Parameter Estimation
133(1)
Random Number Generation
133(1)
Multinomial Distribution
134(3)
Variate Relationships
136(1)
Parameter Estimation
136(1)
Multivariate Normal (Multinormal) Distribution
137(3)
Variate Relationships
138(1)
Parameter Estimation
139(1)
Negative Binomial Distribution
140(5)
Note
142(1)
Variate Relationships
142(2)
Parameter Estimation
144(1)
Random Number Generation
144(1)
Normal (Gaussian) Distribution
145(6)
Variate Relationships
146(4)
Parameter Estimation
150(1)
Random Number Generation
150(1)
Pareto Distribution
151(4)
Note
153(1)
Variate Relationships
153(1)
Parameter Estimation
154(1)
Random Number Generation
154(1)
Poisson Distribution
155(6)
Note
157(1)
Variate Relationships
157(3)
Parameter Estimation
160(1)
Random Number Generation
160(1)
Power Function Distribution
161(4)
Variate Relationships
162(2)
Parameter Estimation
164(1)
Random Number Generation
164(1)
Power Series (Discrete) Distribution
165(2)
Note
166(1)
Variate Relationships
166(1)
Parameter Estimation
166(1)
Rayleigh Distribution
167(3)
Variate Relationships
168(1)
Parameter Estimation
169(1)
Rectangular (Uniform) Continuous Distribution
170(5)
Variatte Relationships
171(3)
Parameter Estimation
174(1)
Random Number Generation
174(1)
Rectangular (Uniform) Discrete Distribution
175(3)
General Form
176(1)
Parameter Estimation
177(1)
Student's t Distribution
178(6)
Variate Relationships
180(3)
Random Number Generation
183(1)
Student's t (Noncentral) Distribution
184(3)
Variate Relationships
186(1)
Triangular Distribution
187(2)
Variate Relationships
188(1)
Random Number Generation
188(1)
von Mises Distribution
189(3)
Note
190(1)
Variate Relationships
191(1)
Parameter Estimation
191(1)
Weibull Distribution
192(12)
Note
193(1)
Variate Relationships
194(1)
Parameter Estimation
194(2)
Random Number Generation
196(1)
Three-Parameter Weibull Distribution
196(1)
Three-Parameter Weibull Random Number Generation
197(1)
Bi-Weibull Distribution
197(2)
Five-Parameter Bi-Weibull Distribution
199(3)
Weibull Family
202(2)
Wishart (Central) Distribution
204(2)
Note
205(1)
Variate Relationships
205(1)
Computing References
206(4)
Statistical Tables
210(10)
Normal Distribution Function
211(1)
Percentiles of the Chi-Squared Distribution
212(2)
Percentiles of the F Distribution
214(4)
Percentiles of the Student's t Distribution
218(1)
Partial Expectations for the Standard Normal Distribution
219(1)
Bibliography 220

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