Foundation item: the Natural Science Foundation of Beijing (No. 1062001);Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(No. 05006011200702).Acknowledgements The authors cordially thank the Associate Editor and Reviewers for their constructive comments which lead to improvement of the manuscript. They are also very grateful to Prof. Adelaide Figueiredo for his help.
In goodness-of-fit tests, Pearson's chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson's chi-squared test depends on the partition of the sample space. Different const...