Rent 9780470390634 | Statistical Distributions | Forbes, Catherine; Evans, Merran; Hastings, Nicholas; Peacock, Brian @knetbooks.com

Summary Table of Contents Author Biography

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 e... MOREach 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.

This fourth edition of Statistical Distributions illustrates the application of statistical methods to research across various disciplines, including medicine, engineering, business/finance, and the social sciences.

A new edition of the trusted guide on commonly used statistical distributions

Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis.

Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features:

A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems
Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions
New coverage of conditional probability, including conditional expectations and joint and marginal distributions
Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions
Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference

Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.

Introduction
Terms and Symbols
Probability, Random Variable, Variate and Number
Range, Quantile, Probability and Domain
Distribution Function and Survival Function
Inverse Distribution and Inverse Survival Function
Probability Density Function and Probability Function
Other Associated Functions and Quantities
General Variate ... MORERelationships
Introduction
Function of a Variate
One-to-One Transformations and Inverses
Variate Relationships Under One-to-One Transformation
Parameters, Variate, and Function Notation
Transformation of Location and Scale
Transformation from the Rectangular Variate
Many-to-One Transformations
Multivariate Distributions
Joint Distributions
Marginal Distributions
Independence
Conditional Distributions
Bayes' Theorem
Functions of a Multivariate
Stochastic Modeling
Introduction
Independent Variates
Mixture Distributions
Skew-Symmetric Distributions
Conditional Skewness
Dependent Variates
Parameter Inference
Introduction
Method of Percentiles Estimation
Method of Moments Estimation
Maximum Likelihood Inference
Bayesian Inference
Bernoulli Distribution
Random Number Generation
Curtailed Bernoulli Trial Sequences
Urn Sampling Scheme
Note
Beta Distribution
Notes on Beta and Gamma Functions
Variate Relationships
Parameter Estimation
Random Number Generation
Inverted Beta Distribution
Noncentral Beta Distribution
Beta Binomial Distribution
Binomial Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Cauchy Distribution
Note
Variate Relationships
Random Number Generation
Generalized Form
Chi-Squared Distribution
Variate Relationships
Random Number Generation
Chi Distribution
Chi-Squared (Noncentral) Distribution
Variate Relationships
DiRichlet Distribution
Variate Relationships
Dirichlet Multinomial Distribution
Empirical Distribution Function
Estimation From Uncensored Data
Estimation From Censored Data
Parameter Estimation
Example
Graphical Method For The Modified Order-Numbers
Model Accuracy
Erlang Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Error Distribution
Note
Variate Relationships
Exponential Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Exponential Family
Members Of The Exponential Family
Univariate One-Parameter Exponential Family
Estimation
Generalized Exponential Distributions
Extreme Value (Gumbel) Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
F (Variance Ratio) or Fisher{ Snedecor Distribution
Variate Relationships
F (Noncentral) Distribution
Variate Relationships
Gamma Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Inverted Gamma Distribution
Normal Gamma Distribution
Generalized Gamma Distribution
Variate Relationships
Geometric Distribution
Notes
Variate Relationships
Random Number Generation
Hypergeometric Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Negative Hypergeometric Distribution
Generalized Hypergeometric (Series) Distribution
Inverse Gaussian (Wald) Distribution
Variate Relationships
Parameter Estimation
Laplace Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
LoGarithmic Series Distribution
Variate Relationships
Parameter Estimation
Logistic Distribution
Notes
Variate Relationships
Parameter Estimation
Random Number Generation
Lognormal Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Multinomial Distribution
Variate Relationships
Parameter Estimation
Multivariate Normal (Multinormal) Distribution
Variate Relationships
Parameter Estimation
Negative Binomial Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Normal (Gaussian) Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Truncated Normal Distribution
Variate Relationships
Pareto Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Poisson Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Power Function Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Power Series (Discrete) Distribution
Note
Variate Relationships
Parameter Estimation
Queuing Formulas
Characteristics of Queuing Systems
Definitions, Notation and Terminology
General Formulas
Some Standard Queuing Systems
Rayleigh Distribution
Variate Relationships
Parameter Estimation
Rectangular (Uniform) Continuous Distribution
Variate Relationships
Parameter Estimation
Random Number Generation
Rectangular (Uniform) Discrete Distribution
General Form
Parameter Estimation
Student's t Distribution
Variate Relationships
Random Number Generation
Student's t (Noncentral) Distribution
Variate Relationships
Triangular Distribution
Variate Relationships
Random Number Generation
von Mises Distribution
Note
Variate Relationships
Parameter Estimation
Weibull Distribution
Note
Variate Relationships
Parameter Estimation
Random Number Generation
Three-Parameter Weibull Distribution
Three-Parameter Weibull Random Number Generation
Bi-Weibull Distribution
Five-Parameter Bi-Weibull Distribution
Weibull Family
Wishart (Central Distribution
Note
Variate Relationships
Statistical Tables
Table of Contents provided by Publisher. All Rights Reserved.

CATHERINE FORBES, PhD, is Senior Lecturer in the Department of Econometrics and Business Statistics at Monash University (Australia). With experience as a statistical consultant for business, manufacturing industries, and social welfare agencies, her research focuses on the areas of Bayesian econometrics, financial modeling, time series analysis, and model selection.

MERRAN EVANS, PhD, is Professor and Pro Vice-Chancellor (Planning and Quality) at Monash University. Dr. Evans has over thirty years of academic experience in the fields of statistics and econometrics.

NICHOLAS HASTINGS, PhD, is Director and Principal Consultant in physical asset management at Albany Interactive Pty Ltd. Dr. Hastings has published extensively in the areas of engineering management and asset management.

BRIAN PEACOCK, PhD, is Founder of Brian Peacock Ergonomics (BPE) Pte. Ltd., a Singapore-based firm that offers ergonomics and human factors education, training, and consulting services. He has previously held consulting positions at General Motors Company and the National Space Biomedical Research Institute/NASA.

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