Machine generated contents note: 1.A Historical Account -- 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 Person'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 -- 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 -- 3.5.1.Introduction -- 3.5.2.Modified chi-squared tests -- 3.5.3.Testing for bivariate circular normality -- 3.5.4.Comparison of different tests -- 3.5.5.Conclusions -- 3.6.Modified chi-squared tests for the exponential distribution -- 3.6.1.Two-parameter exponential distribution -- 3.6.2.Scale-exponential distribution --

Contents note continued: 3.7.Power generalized Weibull distribution -- 3.7.1.Estimation of parameters -- 3.7.2.Modified chi-squared test -- 3.7.3.Evaluation of power -- 3.8.Modified chi-squared goodness of fit test for randomly right censored data -- 3.8.1.Introduction -- 3.8.2.Maximum likelihood estimation for right censored data -- 3.8.3.Chi-squared goodness of fit test -- 3.8.4.Examples -- 3.9.Testing normality for some classical data on physical constants -- 3.9.1.Cavendish's measurements -- 3.9.2.Millikan's measurements -- 3.9.3.Michelson's measurements -- 3.9.4.Newcomb's measurements -- 3.10.Tests based on data on stock returns of two Kazakhastani companies -- 3.10.1.Analysis of daily returns -- 3.10.2.Analysis of weekly returns -- 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 --

Contents note continued: 4.3.Equivalence of Nikulin-Rao-Robson and Hsuan-Robson-Mirvaliev tests for exponential family -- 4.4.Comparisons of some modified chi-squared tests -- 4.4.1.Maximum likelihood estimates -- 4.4.2.Moment-type estimators -- 4.5.Neyman-Pearson classes -- 4.5.1.Maximum likelihood estimators -- 4.5.2.Moment-type estimators -- 4.6.Modified chi-squared rest for three-parameter Weibull distribution -- 4.6.1.Parameter estimation and modified chi-squared tests -- 4.6.2.Power evaluation -- 4.6.3.Neyman-Pearson classes -- 4.6.4.Discussion -- 4.6.5.Concluding remarks -- 5.Modifications Based on UMVUEs -- 5.1.Test for Poisson, binomial, and negative binomial distributions -- 5.2.Chi-squared test for one-parameter exponential family -- 5.3.Revisiting Clarke's data on flying bombs -- 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 --

Contents note continued: 6.5.Combining nonparametric tests -- 6.6.Concluding comments -- 7.Applications of Modified Chi-Squared Tests -- 7.1.Poisson versus binomial: Appointment of judges to the US supreme court -- 7.1.1.Introduction -- 7.1.2.Data to be analyzed -- 7.1.3.Statistical analysis of the data -- 7.1.4.Revisiting the analyses of Wallis and Ulmer -- 7.1.5.Comments about King's exponential Poisson regression model -- 7.1.6.Concluding remarks -- 7.2.Revisiting Rutherford's data -- 7.2.1.Analysis of the data -- 7.2.2.Concluding remarks -- 7.3.Modified tests for the logistic distribution -- 7.4.Modified chi-squared -- 7.4.1.Introduction -- 7.4.2.The NRR, DN and McCulloch tests -- 8.Probability Distributions of Interest -- 8.1.Discrete probability distributions -- 8.1.1.Binomial, geometric, and negative binomial distributions -- 8.1.2.Multinomial distribution -- 8.1.3.Poisson distribution -- 8.2.Continuous probability distributions -- 8.2.1.Exponential distribution --

Contents note continued: 8.2.2.Uniform distribution -- 8.2.3.Triangular distribution -- 8.2.4.Pareto model -- 8.2.5.Normal distribution -- 8.2.6.Multivariate normal distribution -- 8.2.7.Chi-square distribution -- 8.2.8.Non-central chi-square distribution -- 8.2.9.Weibull distribution -- 8.2.10.Generalized power Weibull distribution -- 8.2.11.Birnbaum-Saunders distribution -- 8.2.12.Logistic distribution -- 9.Chi-Squared Tests for Specific Distributions -- 9.1.Test 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 --

Contents note continued: 9.7.1.Test of Greenwood and Nikulin (see Section 3.6.1) -- 9.7.2.Nikulin-Rao-Robson test (see Eq. (3.8) and Section 9.4) -- 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.