Chi-squared goodness of fit tests with applications
"If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the p...
| Autor principal: | |
|---|---|
| Otros Autores: | , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
Academic Press
2013
Waltham, MA : 2013. |
| Edición: | 1st edition |
| Colección: | Gale eBooks
|
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627712806719 |
Tabla de Contenidos:
- Half Title; Title Page; Copyright; Dedication; Contents; Preface; A Historical Account; 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; 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 Test3.5 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; 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 Data3.8.1 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 Kazakhstani Companies; 3.10.1 Analysis of daily returns; 3.10.2 Analysis of weekly returns; Wald's Method and Hsuan-Robson-Mirvaliev Test
- 4.1 Wald's method and moment-type estimators4.2 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; 4.4.1 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 test 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 Discussion4.6.5 Concluding remarks; 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; 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; Applications of Modified Chi-Squared Tests
- 7.1 Poisson versus binomial: Appointment of judges to the US Supreme Court
