Abstract: In this study we develop some useful formulae relating the estimated and the actual values of the parameters of Burr type II and Burr type XII probability distribution functions. These formulae simplify the calculations for Monte Carlo Simulations executed for the estimation of some reference statistics, for example, the reliability function. The reduction of the calculation is possible the parameters of the random number generating function should assume.In some cases of the reliability function, only one Monte Carlo simulation is necessary for a given data sample amplitude. An explanation is made of the use of these formulae when estimating the reliability function.