  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 was 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.
