Handbook of Exponential and Related Distributions for Engineers and Scientists

Published:
November 21, 2005 by Chapman and Hall/CRC - 376 Pages
Author(s):
Nabendu Pal, University of Louisiana at Lafayette, USA; Chun Jin, Central Connecticut State University, New Britain, USA; Wooi K. Lim, William Paterson University, Wayne, New Jersey, USA

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ISBN 9781584881384
Cat# C1380
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Features

  • Provides a complete, concise guide to exponential, gamma, Weibull, and extreme value distributions for immediate applications
  • Builds a foundation in basic mathematics and statistics before discussing the particulars of the distributions
  • Uses many simulations and approximately 100 figures and graphs to illustrate the concepts
  • Provides algorithmic steps that can be used to perform several of the simulations in the book
  • Includes real data sets and many recent research results

    • Summary

    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.

    Table of Contents

    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

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