Methods of investigation and elimination of systematic errors in the realization of pseudo-random variables with heavy-tailed distributions

Shifts arising in generation of random variables, which are obtained by transformation of standard random numbers, with heavy-tailed distributions are investigated. The formula for calculation of deterministic moments shift for a random variable via a discretization spacing of used standard pseudo-random numbers is derived. The deterministic shift is calculated for a mean value of random variables that have the Pareto distribution and realized by the widely accepted inversion technique. The shift calculation results are verified and confirmed experimentally by means of the rapid Monte-Carlo technique - stratification method. By an example of the average queue length calculation, it is demonstrated how the shifts within distributions in queueing systems affect the queueing properties. The universal method for the realization of non-shifted random variables with heavy-tailed distributions, ARAND method, is developed and investigated. The method is based on the use of uniformly distributed between one and zero pseudo-random variables having a variable discretization spacing and represented in floating-point format.