This work considers the problem of modeling of current density fluctuations in conditions of field electron emission. The transmission coefficient of the potential barrier at the emitter surface is calculated with the Runge-Kutta-Nyström method of 12-th order with Dormand-Prince coefficients. The electron supply function is corresponded to metal cathode with tungsten parameters under normal conditions. The emission current density is obtained through the Monte Carlo integration of the external electron distribution. The Shapiro-Wilk normality test for a random current density values is performed. Estimations and confidence intervals for the mean and standard deviation are presented. The dependence of the emission signal noise from the nodes number in a random quadrature formula is constructed.