The evaluation of the systematic uncertainties for the finite MC samples in the presence of negative weights

The analysis of results from HEP experiments often involves the estimates of the composition of the binned data samples, based on Monte Carlo simulations of various sources. Due to a finite statistic of MC samples they have statistical fluctuation. This work proposes the method of incorporating the systematic uncertainties due to finite statistics of MC samples with negative weights. The possible approximations are discussed and the comparison of different methods are presented.