Chi-Squared Goodness of Fit Tests with Applications

1st Edition

Print ISBN: 9780123971944
eBook ISBN: 9780123977830
Imprint: Academic Press
Published Date: 24th January 2013
Page Count: 256
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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 Clar


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© Academic Press 2013
Academic Press
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"The book covers modifications and advances of chi-squared test in cases of various situations. On the whole, the book has a highly mathematical treatment and will be very useful to the researchers working on problems related to chi-squared tests of statistical hypothesis testing."--Zentralblatt MATH, 1276.62027
"The primary purpose of this book is to provide a detailed exploration of the theory, methods, and applications of the chi-squared goodness of fit test first advanced by Karl Pearson over 100 years ago."--Reference and Research, April 2013