Chi-square tests for comparing weighted histograms

Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of a weighted histogram are considered as a sum of random variables with a random number of terms. Generalizations of the classical chi-square test for comparing weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different statistics of events and different weighted functions. The proposed tests can be used for the comparison of experimental data histograms with simulated data histograms as well as for the two simulated data histograms.