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Model of economics - Vіtlіnsky V.V.

3.2. Theoretical basis for the statistical model method

The method of statistical modeling (the Monte Carlo method) is the method of obtaining undetermined (stochastic) economical processes and processes, if they are not affected by the performance of the interconnection system.

You have to use the method of the model for the model process for supporting the stochastic mathematical model and the enumerated characteristics of the whole process. One such viddvorennya possible (vipadkovoy) will become funktsiononuvannya simulated system and call realizatsiyu (chi imitatsіynim run; dali - run).

After the skin run, restore the accuracy of the parameters, which characterize the vipadkova podii (її realizatsіyu). The method to get rid of baggage runs (vipadovyh realizatsiyah) on the first prompted models with the most recent statistical testimony from the past, by identifying the numerical characteristics of the previous view (process) of the viewer. The process of modeling an economical system is reduced to a machine process, which is modeled on the EOM due to the lack of meaning, variability, and generation of them. I will name a simulated model a simulative model. Pershі vіdomostі about the Monte Carlo method boule published in the end of the 40s pp. Twentieth table. The authors of the method є American mathematics - economics J. Neumann and S. Ulam.

The theoretical basis of the statistical model method is the law of great numbers. The theory of great numbers has a large number of laws to keep low theorems for different minds for average values ​​of average results (at the highest great number of points) to underestimated values.

Pіd the law of great numbers rozumіyut kіlka theorems. For example, one of P. L. Chebishev’s theorems is formulated as follows: “For an uninterrupted increase in the number of independent vipers ( n ) the average arithmetic of all systematic errors and differences is small (small), there is a small for the math theory to the mathematical method m x = M (x) of the highest value. ”

It can be written as follows:


de e - yak is pleasingly small to date.

Bernoulli’s theorem is formulated as follows: “For an uninterrupted increase in the number of independent samples ( n ) for one and these very minds, the frequency is visible Nastanya vipadkovo podії zbіgaєsya for ymovіrnіstyu to r , so that:


de e - yak is pleasingly small to date. ”

Proceeding with the following theorem for the rejection of the performance of the singing system, for the purpose of the performance of the operating system , enumerate the ideal frequency for real estate, scho dorіvnyuє n . The results are averaged and won’t be close to gaining the shukans of the system’s system. What is greater is n , and what is more exact is the result of the calculation of these indices. Tse is easy to bring.

It is permissible, however, that the requirement of mathematical significance is necessary for the singing vipadkov value. Pidbermo taku vipadkova value x, shchob

M (x) = m , and D (x) = b 2,

de b 2 is the significant value of the dispersion of the vipadkovo value x.

Rosganymo postіnovnіst n independent vipadkovyh quantities , rozpodil іmovіrnosti yak zbіgaєatsya with rozpodil x. As far as n є to finish the great, then it is necessary with the central boundary theorem

will be approximately normal rozpodil with parameters a = nm ; s2 = nb 2.

3 rules "trih sigma" whip,


Razdivlivshi nerve, schto roshtashovannoy at the arches, on the n , from the middle of the eve to the nerve of the most self-sustaining:

You can record the following in the video:


Spivvydnoshennya (3.4) viznachaє method of calculating the average value m і otsіnku bend. It can be seen from (3.4) that the average arithmetic realization of the vipadka value x is close to the most recognizable number m . З імовірністю р = 0,997 I can’t overdo such an approximationлиж . Obviously, how can bending be straightforward to zero with zero n , which should be brought up.

Razv'yazuvannya tasks by the method of statistical modeling of the plowє in this:

  • opratsyuvannya y pudova structural diagram of the process, the manifestation of the main vzamozv'yazkіv;
  • formalization described the process;
  • a model of vipadkivka yavishcha (vipadkovy podi, vipadkovy values, vipadkovy functions), scho prismanny doslіdzhuvanі system;
  • I model the process of the functionalization of the system (in the past, give it a second note, but remove it in the front step) - I will complete the process in the most detailed way to the detailed structural diagram and formalized description (imitated);
  • the accumulated results of the modeling (imitation runs), the statistical analysis, the analysis and interpretation of them.

It means that if you are firmly convinced of the characteristics of a simulated system and are guilty of being guided by the results of vidpovidnyh translations for an additional method of mathematical statistics.

Oskilka vipadkovі podії vipadkov_ functions can be served on vikoristanni vipadkovyh values, then the first model vipadkovy podii and vipadkovy functions carried out for the help of vipadkovy values.