МОДЕЛЮВАННЯ НЕСИМЕТРИЧНО РОЗПОДІЛЕНИХ ПРОЦЕСІВ

Abstract

The article deals with the problems of modeling asymmetrically distributed stochastic processes and assessing the quality of the modeling process based on the use of the Pearson chi-square criterion. The problems that arise in each individual case of modeling are identified. As a method of generating an output stream of random numbers distributed according to a given law of probability distribution, the method of inverse functions is proposed, and as a generator of the input stream, it is proposed to use a stream generated by the Mersenne generator. The analysis of research methods and evaluation of computer models of stochastic processes is given and the choice of a nonparametric research method based on histograms is substantiated. Suggestions on the choice of their main parameters are provided: the size of the interval for separating the statistical set of values of the output stream of the model and the number of such intervals, calculated on the basis of the size of the statistical sample. It is shown that the quality of statistical material significantly affects the success of modeling. In the case of an asymmetric nature of the distribution of the model's output stream, the accuracy of calculating the chi-square exponent is significantly affected by those values that fall into the extreme intervals of the histogram. It is shown that the reason for this is the incommensurability of their values with the values in the central part of the histogram and this is a separate modeling problem, as a solution to which there can be filtering of the statistical set, preceding the determination of the quality indicator. The sequence of procedures for forming a model of a stochastic process and processing the results of calculating the parameters of the histogram is determined.