Goodness of fit tests for 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 experiment with random events that have weights. In this paper the bin contents of weighted histogram are considered as a sum of random variables with random number of terms. Goodness of fit tests for weighted histograms and for weighted histograms with unknown normalization are proposed. Sizes and powers of the tests are investigated numerically.