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The pseudo-randomly distributed numbers always require to pass any test, in order to obtain a valid sequence of random numbers. There have been used mainly the different types of checking the pseudo-randomly equally distributed numbers.
The positive aspect is: the accuracy of method and avoidance of the design tables, which are mainly used in the imitation programming languages, which excludes memory loading and executing extra work, as well as generation of random numbers with any distribution law, obtaining any accuracy by increasing the number of interval, there is only a need for one random number and a simple transformation.
There have been applied three types of assessment – appropriate with an average integral one, not average weighted magnitude and the arithmetic mean. Since statistical information is gathered within the discrete time intervals, the mean arithmetic assessment of mathematical expectation is the basic one with mathematical expectation assessment methods. The auto-correlation function, at the initial stage, is in a declining trend of coordinates, and obviously, it is decreasing slowly, and the Lagu erre function has the same property, so we make approximation of the Lagu erre first-order autocorrelation function.
We assess the average integral and mean arithmetic mathematical expectation by comparing the dispersion values, with the assumption that the smaller the dispersion the more accurate assessment. Therefore, the type of the correlation function influences the length of an initial interval and the permissible value of mathematical expectation.