The modeling of electron energy distributions for the field flat cathode was performed. Numerical experiment parameters respond tungsten under normal conditions. Random samples of particle energy values were obtained with the transformation method. For the integration of the distributions Simpson's rule and Bode's rule were used. The possibility of samples combining with different values of emission parameters was established. Mann-Whitney (Wilcoxon) nonparametric rank-sum test was used for the statistical hypothesis testing. The intervals for parameters within which the samples can be considered as extracted from the same population were found.