Binning in the chi-square goodness-of-fit test

Abstract

One of the most commonly used goodness-of-fit tests is based on Pearson's chi-square statistic. Since this requires class intervals for the data, questions arise with respect to the method of estimation, types, and the number of classes to use. In one dimension, standard recommendations are to use intervals with the same probability or the same size. A combination of these two was studied, and a method that automatically finds the optimal bin type and the number of bins is presented. To make this possible, an improved computational tool is also presented.