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Chi-Squared Goodness of Fit Tests with Applications

Book Description

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.



  • 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

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Preface
  7. Chapter 1. A Historical Account
    1. References
  8. Chapter 2. Pearson’s Sum and Pearson-Fisher Test
    1. 2.1 Pearson’s chi-squared sum
    2. 2.2 Decompositions of Pearson’s chi-squared sum
    3. 2.3 Neyman-Pearson classes and applications of decompositions of Pearson’s sum
    4. 2.4 Pearson-Fisher and Dzhaparidze-Nikulin tests
    5. 2.5 Chernoff-Lehmann theorem
    6. 2.6 Pearson-Fisher test for random class end points
    7. References
  9. Chapter 3. Wald’s Method and Nikulin-Rao-Robson Test
    1. 3.1 Wald’s method
    2. 3.2 Modifications of Nikulin-Rao-Robson Test
    3. 3.3 Optimality of Nikulin-Rao-Robson Test
    4. 3.4 Decomposition of Nikulin-Rao-Robson Test
    5. 3.5 Chi-Squared Tests for Multivariate Normality
    6. 3.6 Modified Chi-Squared Tests for The Exponential Distribution
    7. 3.7 Power Generalized Weibull Distribution
    8. 3.8 Modified chi-Squared Goodness of Fit Test for Randomly Right Censored Data
    9. 3.9 Testing Normality for Some Classical Data on Physical Constants
    10. 3.10 Tests Based on Data on Stock Returns of Two Kazakhstani Companies
    11. References
  10. Chapter 4. Wald’s Method and Hsuan-Robson-Mirvaliev Test
    1. 4.1 Wald’s method and moment-type estimators
    2. 4.2 Decomposition of Hsuan-Robson-Mirvaliev test
    3. 4.3 Equivalence of Nikulin-Rao-Robson and Hsuan-Robson-Mirvaliev tests for exponential family
    4. 4.4 Comparisons of some modified chi-squared tests
    5. 4.5 Neyman-Pearson classes
    6. 4.6 Modified chi-squared test for three-parameter Weibull distribution
    7. References
  11. Chapter 5. Modifications Based on UMVUEs
    1. 5.1 Tests for Poisson, binomial, and negative binomial distributions
    2. 5.2 Chi-squared tests for one-parameter exponential family
    3. 5.3 Revisiting Clarke’s data on flying bombs
    4. References
  12. Chapter 6. Vector-Valued Tests
    1. 6.1 Introduction
    2. 6.2 Vector-valued tests: an artificial example
    3. 6.3 Example of Section 2.3 revisited
    4. 6.4 Combining nonparametric and parametric tests
    5. 6.5 Combining nonparametric tests
    6. 6.6 Concluding comments
    7. References
  13. Chapter 7. Applications of Modified Chi-Squared Tests
    1. 7.1 Poisson versus binomial: Appointment of judges to the US Supreme Court
    2. 7.2 Revisiting Rutherford’s data
    3. 7.3 Modified tests for the logistic distribution
    4. 7.4 Modified chi-squared tests for the inverse Gaussian distribution
    5. References
  14. Chapter 8. Probability Distributions of Interest
    1. 8.1 Discrete probability distributions
    2. 8.2 Continuous probability distributions
    3. References
  15. Chapter 9. Chi-Squared Tests for Specific Distributions
    1. 9.1 Tests for Poisson, binomial, and “binomial” approximation of Feller’s distribution
    2. 9.2 Elements of matrices K, B, C, and V for the three-parameter Weibull distribution
    3. 9.3 Elements of matrices J and B for the Generalized Power Weibull distribution
    4. 9.4 Elements of matrices J and B for the two-parameter exponential distribution
    5. 9.5 Elements of matrices B, C, K, and V to test the logistic distribution
    6. 9.6 Testing for normality
    7. 9.7 Testing for exponentiality
    8. 9.8 Testing for the logistic
    9. 9.9 Testing for the three-parameter Weibull
    10. 9.10 Testing for the Power Generalized Weibull
    11. 9.11 Testing for two-dimensional circular normality
    12. References
  16. Bibliography
  17. Index