Theoretical and Statistical Modeling of Experimental Data Application for the Development of Mathematically Interpreted Interconnection of the Dynamic Elements of the Meso- and Macro-levels of the Modern Economy

This article provides an economic and mathematical background for experiments aimed at systematizing empirical data that can serve as the basis for the mathematical interpretation of models of internal interconnection between dynamic elements of economic systems of different levels, and for the modeling of external influences on an entire system of a national economy. This would eventually allow the development of a numerical implementation of the solution to the problem of dynamic stability of a national economy mechanism under the influence of external stochastic factors.

Aim. This study aims to propose an apparatus substantiated from the perspective of theoretical statistics for the integration of discrete experimental data examined in the form of one or several factors as independent, normally distributed random values, with possible application of the approach in the development of internal interconnection of complex dynamic economic systems, combined with the possibility of testing the statistical hypotheses determined during such modeling.

Tasks. This study interprets the aforementioned research using the apparatus of modern mathematics and a combination of mathematical and instrumental methods in economics. This allows a modern economic theorist to make a swift transition to practical methods and techniques for obtaining the entire spectrum of the necessary mathematical dependencies (functions) for the numerical implementation of the solution to the problem of dynamic stability and for analysis of the problem of boundary conditions of the entire mechanism of a national economy under the influence of external stochastic factors.

Methods. In terms of methodology, the author appeals to the problem of synthesis of discrete experimental data, the theoretical and statistical interpretation of which forms the basis for relatively accurate mathematical determination of functional relationships that serve as the basis for the mathematical theory of stability and transition processes in complex multilevel hierarchy systems.

Results. During the study, the author concludes that the process of organizing and planning experiments is a predecessor step in terms of theory and statistics. This step is essential to obtain statistically significant combinations of methods and techniques for the concretization, specification, and testing of statistical hypotheses that are fundamental to the determination of spectral functions for modeling the entire system of internal and external factors that provide a numerical solution to the problem of dynamic stability of the complex and multilevel system of national economy.

Conclusion. As a result, the study summarizes the problems of testing the hypothesis of equality of mean values of multiple normally distributed random values with equal variance for the cases, considering the influence of one or multiple factors on the entire system. The study also shows that the hypotheses of equality of mean values of multiple factors can be tested using the Fisher–Snedecor distribution. The unbiased variance estimate is compared to the variance determined using the Fisher–Snedecor distribution, which allows the author to accept or reject the hypothesis depending on the significance of its deviation from the ratio between the last estimate to the residual variance estimate. Using this data, it is possible to plot valid functional dependencies linking, with certain assumptions, the control and controlled parameters of economic systems even under conditions of uncertainty.

1. Kolemaev V. A. Ekonomiko-matematicheskoe modelirovanie. Modelirovanie makroekonomicheskikh protsessov i sistem [Economic-mathematical modeling. Modeling of macroeconomic processes and systems]. Moscow, YuNITI-DANA Publ., 2005. 295 p.

2. Fisher R. A. The design of experiments. London, Oliver and Boyd Publ., 1935. 260 p.

3. Kobzar’ A. I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov [Applied mathematical statistics. For engineers and scientists]. Moscow, FIZMATLIT Publ., 2012. 816 p.

4. Mann H. B. Analysis and design of experiments: Analysis of variance and analysis of variance designs. New York, Dover Publ., 1949. 195 p.

5. Fréchet M. Généralités sur les probabilités. Eléments aléatoires [Overview of probabilities. Random elements]. Paris. Gauthier-Villars Publ., 1950. 355 p.