Details of Research Outputs

The classical Pearson-Fisher chi-square test is a general approach to testing goodness-of-fit for univariate data. There is a considerable amount of discussion on how to effectively apply this test to practical goodness-of-fit problems in the literature. However, the choice of optimal grouping intervals in constructing the chi-square statistic still remains arguable and uncertain. Based on the statistical principle of defining the mean-square-error representative points, we propose to employ the statistical representative points to construct the Pearson-Fisher chi-square test. We carry out an extensive Monte Carlo study on the performance of the new-type of chi-square test by focusing on some location-scale distributions. It shows that our construction of the chi-square test outperforms the traditional construction of the same test by using equiprobable points for the grouping intervals in the sense of type I error control and power against some general alternative distributions.