Chi-square goodness of fit tests for weighted histograms. Review and improvements

Abstract: Weighted histograms are used for the estimation of probability density functions. Computer simulation is the main domain of application of this type of histogram. A review of chi-square goodness of fit tests for weighted histograms is presented in this paper. Improvements are proposed to these tests that have size more close to its nominal value. Numerical examples are presented in this paper for evaluation of tests and to demonstrate various applications of tests.