
Chi-Squared Goodness of Fit Tests with Applications
Description
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
Readership
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

Affiliations and Expertise
Vassilly Voinov
M.S Nikulin
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