Handbook of Exponential and Related Distributions for Engineers and Scientists

Handbook of Exponential and Related Distributions for Engineers and Scientists

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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.show more

Product details

  • Hardback | 376 pages
  • 218.44 x 279.4 x 27.94mm | 1,406.13g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 88 black & white illustrations, 32 black & white tables, 4 black & white halftones
  • 1584881380
  • 9781584881384

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 Indexshow more