Statistical Distributions

This new edition continues to illustrate the application of statistical methods to research across various disciplines, including medicine, engineering, business/finance, and the social sciences. Thoroughly revised and updated, the authors have refreshed this book to reflect the changes and current trends in statistical distibution theory that have occured since the publication of the previous edition eight years ago. The introductory chapters introduce the fundamental concepts of the distributions and the relationships between variables. For each distribution that follows, the key formulae, tables and diagrams are presented in a concise, user–friendly format. Key facts and formulas for forty major probability distributions are presented, making the book an ideal introduction to the general theory of statistical distributions as well as a quick reference on its basic principles. 
Newly added coverage includes the exploration of connections between distributions using conditioning; discussion of distributions not addressed in the previous edition (such as Generalized Student–t, binomial distribution, and triangular distribution); and a thorough review of conditional probability, conditional expectations, and joint and marginal distributions. A new chapter on statistical inference has also been added, illustrating modeling strategies and the use of conditioning in model building, while also presenting an overview of both classical statistical inference and Bayesian statistical inference.

Spis treści:
1 Introduction.
2 Terms and Symbols.
2.1 Probability, Random Variable, Variate and Number.
2.2 Range, Quantile, Probability and Domain.
2.3 Distribution Function and Survival Function.
2.4 Inverse Distribution and Inverse Survival Function.
2.5 Probability Density Function and Probability Function.
2.6 Other Associated Functions and Qua ntities.
3 General Variate Relationships.
3.1 Introduction.
3.2 Function of a Variate.
3.3 One–to–One Transformations and Inverses.
3.4 Variate Relationships Under One–to–One Transformation.
3.5 Parameters, Variate, and Function Notation.
3.6 Transformation of Location and Scale.
3.7 Transformation from the Rectangular Variate.
3.8 Many–to–One Transformations.
4 Multivariate Distributions.
4.1 Joint Distributions.
4.2 Marginal Distributions.
4.3 Independence.
4.4 Conditional Distributions.
4.5 Bayes′ Theorem.
4.6 Functions of a Multivariate.
5 Stochastic Modeling.
5.1 Introduction.
5.2 Independent Variates.
5.3 Mixture Distributions.
5.4 Skew–Symmetric Distributions.
5.5 Conditional Skewness.
5.6 Dependent Variates.
6 Parameter Inference.
6.1 Introduction.
6.2 Method of Percentiles Estimation.
6.3 Method of Moments Estimation.
6.4 Maximum Likelihood Inference.
6.5 Bayesian Inference.
7 Bernoulli Distribution.
7.1 Random Number Generation.
7.2 Curtailed Bernoulli Trial Sequences.
7.3 Urn Sampling Scheme.
7.4 Note.
8 Beta Distribution.
8.1 Notes on Beta and Gamma Functions.
8.2 Variate Relationships.
8.3 Parameter Estimation.
8.4 Random Number Generation.
8.5 Inverted Beta Distribution.
8.6 Noncentral Beta Distribution.
8.7 Beta Binomial Distribution.
9 Binomial Distribution.
9.1 VARIATE RELATIONSHIPS.
9.2 PARAMETER ESTIMATION.
9.3 RANDOM NUMBER GENERATION.
10 Cauchy Distribution.
10.1 NOTE.
10.2 VARIATE RELATIONSHIPS.
10.3 RANDOM NUMBER GENERATION.
10.4 GENERALIZED FORM.
11 Chi–Squared Distribution.
11.1 VARIATE RELATIONSHIPS.
11.2 RANDOM NUMBER GENERATION.
11.3 CHI DISTRIBUTION.
12 Chi–Squared (Noncentral) Distribution.
12.1 VARIATE RELATIONSHIPS.
13 Dirichlet Dis tribution.
13.1 VARIATE RELATIONSHIPS.
13.2 DIRICHLET MULTINOMIAL DISTRIBUTION.
14 Empirical Distribution Function.
14.1 ESTIMATION FROM UNCENSORED DATA.
14.2 ESTIMATION FROM CENSORED DATA.
14.3 PARAMETER ESTIMATION.
14.4 EXAMPLE.
14.5 GRAPHICAL METHOD FOR THE MODIFIED ORDER–NUMBERS.
14.6 MODEL ACCURACY.
15 Erlang Distribution.
15.1 VARIATE RELATIONSHIPS.
15.2 PARAMETER ESTIMATION.
15.3 RANDOM NUMBER GENERATION.
16 Error Distribution.
16.1 NOTE.
16.2 VARIATE RELATIONSHIPS.
17 Exponential Distribution.
17.1 NOTE.
17.2 VARIATE RELATIONSHIPS.
17.3 PARAMETER ESTIMATION.
17.4 RANDOM NUMBER GENERATION.
18 Exponential Family.
18.1 MEMBERS OF THE EXPONENTIAL FAMILY.
18.2 UNIVARIATE ONE–PARAMETER EXPONENTIAL FAMILY.
18.3 ESTIMATION.
18.4 GENERALIZED EXPONENTIAL DISTRIBUTIONS.
19 Extreme Value (Gumbel) Distribution.
19.1 NOTE.
19.2 VARIATE RELATIONSHIPS.
19.3 PARAMETER ESTIMATION.
19.4 RANDOM NUMBER GENERATION.
20 F (Variance Ratio) or Fisher{ Snedecor Distribution.
20.1 VARIATE RELATIONSHIPS.
21 F (Noncentral) Distribution.
21.1 VARIATE RELATIONSHIPS.
22 Gamma Distribution.
22.1 VARIATE RELATIONSHIPS.
22.2 PARAMETER ESTIMATION.
22.3 RANDOM NUMBER GENERATION.
22.4 INVERTED GAMMA DISTRIBUTION.
22.5 NORMAL GAMMA DISTRIBUTION.
22.6 GENERALIZED GAMMA DISTRIBUTION.
22.6.1 Variate Relationships.
23 Geometric Distribution.
23.1 NOTES.
23.2 VARIATE RELATIONSHIPS.
23.3 RANDOM NUMBER GENERATION.
24 Hypergeometric Distribution.
24.1 NOTE.
24.2 VARIATE RELATIONSHIPS.
24.3 PARAMETER ESTIMATION.
24.4 RANDOM NUMBER GENERATION.
24.5 NEGATIVE HYPERGEOMETRIC DISTRIBUTION.
24.6 GENERALIZED HYPERGEOMETRIC (SERIES) DISTRIBUTION.
25 Inverse Gaussian (Wald) Distribution.
25.1 VARIATE RELATIONSHIPS.
25.2 PARAMETER ESTIMATION.
26 Lapl ace Distribution.
26.1 VARIATE RELATIONSHIPS.
26.2 PARAMETER ESTIMATION.
26.3 RANDOM NUMBER GENERATION.
27 Logarithmic Series Distribution.
27.1 VARIATE RELATIONSHIPS.
27.2 PARAMETER ESTIMATION.
28 Logistic Distribution.
28.1 NOTES.
28.2 VARIATE RELATIONSHIPS.
28.3 PARAMETER ESTIMATION.
28.4 RANDOM NUMBER GENERATION.
29 Lognormal Distribution.
29.1 VARIATE RELATIONSHIPS.
29.2 PARAMETER ESTIMATION.
29.3 RANDOM NUMBER GENERATION.
30 Multinomial Distribution.
30.1 VARIATE RELATIONSHIPS.
30.2 PARAMETER ESTIMATION.
31 Multivariate Normal (Multinormal) Distribution.
31.1 VARIATE RELATIONSHIPS.
31.2 PARAMETER ESTIMATION.
32 Negative Binomial Distribution.
32.1 NOTE.
32.2 VARIATE RELATIONSHIPS.
32.3 PARAMETER ESTIMATION.
32.4 RANDOM NUMBER GENERATION.
33 Normal (Gaussian) Distribution.
33.1 VARIATE RELATIONSHIPS.
33.2 PARAMETER ESTIMATION.
33.3 RANDOM NUMBER GENERATION.
33.4 TRUNCATED NORMAL DISTRIBUTION.
33.5 VARIATE RELATIONSHIPS.
34 Pareto Distribution.
34.1 NOTE.
34.2 VARIATE RELATIONSHIPS.
34.3 PARAMETER ESTIMATION.
34.4 RANDOM NUMBER GENERATION.
35 Poisson Distribution.
35.1 NOTE.
35.2 VARIATE RELATIONSHIPS.
35.3 PARAMETER ESTIMATION.
35.4 RANDOM NUMBER GENERATION.
36 Power Function Distribution.
36.1 VARIATE RELATIONSHIPS.
36.2 PARAMETER ESTIMATION.
36.3 RANDOM NUMBER GENERATION.
37 Power Series (Discrete) Distribution.
37.1 NOTE.
37.2 VARIATE RELATIONSHIPS.
37.3 PARAMETER ESTIMATION.
38 Queuing Formulas.
38.1 Characteristics of Queuing Systems.
38.2 Definitions, Notation and Terminology.
38.3 General Formulas.
38.4 Some Standard Queuing Systems.
39 Rayleigh Distribution.
39.1 VARIATE RELATIONSHIPS.
39.2 PARAMETER ESTIMATION.
40 Rectangular (Uniform) Continuous Distribution.
40.1 VARIATE R