Handbook of Exponential and Related Distributions for Engineers and Scientists

ISBN-13: 9781584881384 / Angielski / Twarda / 2005 / 376 str.

Nabendu Pal; Chun Jin; Wooi K. Lim

Opis

The normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of Exponential and Related Distributions for Engineers and Scientists provides a concise, carefully selected presentation of the properties and principles of selected distributions that are most useful for application in the sciences and engineering.
The book begins with all the basic mathematical and statistical background necessary to select the correct distribution to model real-world data sets. This includes inference, decision theory, and computational aspects including the popular Bootstrap method. The authors then examine four skewed distributions in detail: exponential, gamma, Weibull, and extreme value. For each one, they discuss general properties and applicability to example data sets, theoretical characterization, estimation of parameters and related inferences, and goodness of fit tests. The final chapter deals with system reliability for series and parallel systems.
Presenting methods based on statistical simulations and numerical computations, the Handbook of Exponential and Related Distributions for Engineers and Scientists supplies hands-on tools for applied researchers in need of practical tools for data analysis.

Spis treści

Acronyms
Notations
List of Figures
List of Tables
GENERAL STATISTICAL THEORY
Basic Concepts
The System of Real Numbers
Some Useful Algebraic Results
Set Theory
Introduction to Probability Theory
Random Variables
Joint Probability Distributions
Moment Generating Function
Order Statistics
Characteristic Function

Some Common Probability Distributions
Discrete Distributions
Continuous Distributions
Some Limit Theorems

Concepts of Statistical Inference
Introduction
Sufficiency and Completeness
Methods of Estimation
Methods of Evaluating Estimators
Elements of Hypothesis Testing
Set (or Interval) Estimation

Elements of Decision Theory
Introduction
Optimality Criteria
Loss Functions
Admissible, Minimax and Bayes Rules

Computational Aspects
Preliminaries
Numerical Integration
Monte-Carlo Simulation
Bootstrap Method of Resampling
Testing and Interval Estimation Based on Computations

EXPONENTIAL AND OTHER POSITIVELY SKEWED DISTRIBUTIONS WITH APPLICATIONS
Exponential Distribution
Preliminaries
Characterization of Exponential Distribution
Estimation of Parameter(s)
Goodness of Fit Tests for Exponential Distributions

Gamma Distribution
Preliminaries
Characterization of Gamma Distribution
Estimation of Parameters
Goodness of fit Tests for Gamma Distribution

Weibull Distribution
Preliminaries
Characterization of Weibull Distribution
Estimation of Parameters
Goodness of Fit Tests for Weibull Distribution

Extreme Value Distributions
Preliminaries
Characterizations of Extreme Value Distributions
Estimation of Parameters
Goodness of Fit Tests for Extreme Value Distributions

System Reliability
Preliminaries
Single Component Systems
Reliability of a Series System with Componentwise Data
Reliability of a Parallel System with Componentwise Data
Bibliography
Selected Statistical Tables
Index

O autorze

Nabendu Pal, Chun Jin, Wooi K. Lim