2016, Vol. 3, No. 3. - go to content...

Метаданные этой статьи так же доступны на русском языке DOI: 10.15862/06TS316 (https://doi.org/10.15862/06TS316)

For citation:

Stolyarov V.V., Shchegoleva N.V. [Examples of probability calculation in processing digital data using the normal and binomial distributions] Russian Journal of Transport Engineering, 2016, Vol. 3, No. 3. Available at: https://t-s.today/PDF/06TS316.pdf (in Russian). DOI: 10.15862/06TS316

## Examples of probability calculation in processing digital data using the normal and binomial distributions

Stolyarov Viktor Vasilevich
Yuri Gagarin state technical university of Saratov, Russia, Saratov
E-mail: stolyarov_v_v@mail.ru

Shchegoleva Natalia Vyacheslavovna
Yuri Gagarin state technical university of Saratov, Russia, Saratov
E-mail: Shegoleva123@mail.ru

Abstract. In solving problems associated with statistical processing of discrete integer values varying sequentially per unit it is handier to use conversions of A. Moivre that were made for the transition from the discrete binomial distribution to continuous distribution later called normal. The normal distribution law of Moivre (Moivre — Laplace, Gauss) is widely used in the statistical processing of continuous variables and undeservedly seldom used in original form suitable for processing discrete integer values varying per unit. In a series of articles the authors show the advantages of this method in solving applied problems related to the processing of integer variables. This article in compressed form shows the basic calculation formulae, allowing to use the opportunities of continuous distribution while statistical processing of the integer variables. Examples of such calculations are presented from different branches of science or technology: management, technical (on the subject of transport construction) and community activities. In all the examples of the probability calculation while processing of discrete data the comparison of results obtained for the normal and binomial distribution was performed. Replacement of the binomial distribution by the normal law leads to a significant reduction in the volume of calculations without dilution of precision of the obtained results under the control of applicability of the normal distribution according to the formula of the boundary condition.

Keywords: probability density; Laplace function; function of the normal distribution; binomial distribution of discrete integer values; mathematical expectation and mean value; mean-square deviation; independent variables or factors; critical parameters; limit of the applicability of the normal law instead of binomial distribution 