A Comparative Study of Some Modified Chi-Squared Tests

Abstract

Some recent results in the theory and applications of modified chi-squared goodness-of-fit tests are briefly discussed. It seems that for the first time power of modified chi-squared type tests for the logistic and three-parameter Weibull distributions based on moment type estimators is studied. Power of different modified tests against some alternatives for equiprobable fixed or random grouping intervals, and for Neyman–Pearson classes is investigated. It is shown that power of test statistic essentially depends on the quantity of Fisher's sample information this statistic uses. Some recommendations on implementing modified chi-squared type tests are given.

Keywords:

• Anderson–Darling test
• Equiprobable and Neyman–Pearson classes
• Maximum likelihood and moment' type estimators
• Minimum chi-squared
• Mirvaliev's test
• Pearson–Fisher's test
• Pearson's chi-squared test
• Power of modified chi-squared tests
• Rao–Robson–Nikulin test

Mathematics Subject Classification:

• 62F03
• 62G10
• 62F10

Acknowledgments

The authors are grateful to Prof. M. Nikulin who recommended us to investigate Neyman–Pearson classes and to Ivan Kharitonov for producing a large part of the simulation. We also would like to thank referees and N. Balakrishnan for valuable comments, which helped us to improve the presentation.