Chi-Squared Goodness of Fit Tests with Applications

Chi-Squared Goodness of Fit Tests with Applications

1st Edition - January 24, 2013

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  • Authors: N. Balakrishnan, Vassilly Voinov, M.S Nikulin
  • eBook ISBN: 9780123977830
  • Hardcover ISBN: 9780123971944

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Chi-Squared Goodness of Fit Tests with Applications provides a thorough and complete context for the theoretical basis and implementation of Pearson’s monumental contribution and its wide applicability for chi-squared goodness of fit tests. The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods. The historical context, especially Chapter 7, provides great insight into importance of this subject with an authoritative author team.  This reference includes the most recent application developments in using these methods and models.

Key Features

  • Systematic presentation with interesting historical context and coverage of the fundamentals of the subject
  • Presents modern model validity methods, graphical techniques, and computer-intensive methods
  • Recent research and a variety of open problems
  • Interesting real-life examples for practitioners


Researchers, professionals and specialists in applied mathematical statistics; graduate students and postgraduate students interested in problems of applied mathematical statistics; students and postgraduate students who use methods of statistical analysis in processing of experimental data; -specialists (researchers) who analyze data of experimental investigations (in applications).

Table of Contents

    • Dedication
    • Preface
    • Chapter 1. A Historical Account
      • References
    • Chapter 2. Pearson’s Sum and Pearson-Fisher Test
      • 2.1 Pearson’s chi-squared sum
      • 2.2 Decompositions of Pearson’s chi-squared sum
      • 2.3 Neyman-Pearson classes and applications of decompositions of Pearson’s sum
      • 2.4 Pearson-Fisher and Dzhaparidze-Nikulin tests
      • 2.5 Chernoff-Lehmann theorem
      • 2.6 Pearson-Fisher test for random class end points
      • References
    • Chapter 3. Wald’s Method and Nikulin-Rao-Robson Test
      • 3.1 Wald’s method
      • 3.2 Modifications of Nikulin-Rao-Robson Test
      • 3.3 Optimality of Nikulin-Rao-Robson Test
      • 3.4 Decomposition of Nikulin-Rao-Robson Test
      • 3.5 Chi-Squared Tests for Multivariate Normality
      • 3.6 Modified Chi-Squared Tests for The Exponential Distribution
      • 3.7 Power Generalized Weibull Distribution
      • 3.8 Modified chi-Squared Goodness of Fit Test for Randomly Right Censored Data
      • 3.9 Testing Normality for Some Classical Data on Physical Constants
      • 3.10 Tests Based on Data on Stock Returns of Two Kazakhstani Companies
      • References
    • Chapter 4. Wald’s Method and Hsuan-Robson-Mirvaliev Test
      • 4.1 Wald’s method and moment-type estimators
      • 4.2 Decomposition of Hsuan-Robson-Mirvaliev test
      • 4.3 Equivalence of Nikulin-Rao-Robson and Hsuan-Robson-Mirvaliev tests for exponential family
      • 4.4 Comparisons of some modified chi-squared tests
      • 4.5 Neyman-Pearson classes
      • 4.6 Modified chi-squared test for three-parameter Weibull distribution
      • References
    • Chapter 5. Modifications Based on UMVUEs
      • 5.1 Tests for Poisson, binomial, and negative binomial distributions
      • 5.2 Chi-squared tests for one-parameter exponential family
      • 5.3 Revisiting Clarke’s data on flying bombs
      • References
    • Chapter 6. Vector-Valued Tests
      • 6.1 Introduction
      • 6.2 Vector-valued tests: an artificial example
      • 6.3 Example of Section 2.3 revisited
      • 6.4 Combining nonparametric and parametric tests
      • 6.5 Combining nonparametric tests
      • 6.6 Concluding comments
      • References
    • Chapter 7. Applications of Modified Chi-Squared Tests
      • 7.1 Poisson versus binomial: Appointment of judges to the US Supreme Court
      • 7.2 Revisiting Rutherford’s data
      • 7.3 Modified tests for the logistic distribution
      • 7.4 Modified chi-squared tests for the inverse Gaussian distribution
      • References
    • Chapter 8. Probability Distributions of Interest
      • 8.1 Discrete probability distributions
      • 8.2 Continuous probability distributions
      • References
    • Chapter 9. Chi-Squared Tests for Specific Distributions
      • 9.1 Tests for Poisson, binomial, and “binomial” approximation of Feller’s distribution
      • 9.2 Elements of matrices K, B, C, and V for the three-parameter Weibull distribution
      • 9.3 Elements of matrices J and B for the Generalized Power Weibull distribution
      • 9.4 Elements of matrices J and B for the two-parameter exponential distribution
      • 9.5 Elements of matrices B, C, K, and V to test the logistic distribution
      • 9.6 Testing for normality
      • 9.7 Testing for exponentiality
      • 9.8 Testing for the logistic
      • 9.9 Testing for the three-parameter Weibull
      • 9.10 Testing for the Power Generalized Weibull
      • 9.11 Testing for two-dimensional circular normality
      • References
    • Bibliography
    • Index

Product details

  • No. of pages: 256
  • Language: English
  • Copyright: © Academic Press 2013
  • Published: January 24, 2013
  • Imprint: Academic Press
  • eBook ISBN: 9780123977830
  • Hardcover ISBN: 9780123971944

About the Authors

N. Balakrishnan

N. Balakrishnan
Narayanaswamy Balakrishnan, Distinguished University Professor, is in the Department of Mathematics and Statistics McMaster University Hamilton, Ontario, Canada. Professor Balakrishnan is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with 16 authored books, 4 authored handbooks, and 27 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis, and was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics, and in 2016 was awarded an Honorary Doctorate for The National and Kapodistrian University of Athens, Athens, Greece.

Affiliations and Expertise

Professor of Statistics, Department of Mathematics and Statistics McMaster University Hamilton, Ontario, Canada; visiting Professor, King Abdulaziz University, Jeddah, Saudi Arabi

Vassilly Voinov

M.S Nikulin

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