Software implementation of the analysis of uniformly and normally distributed random variables for deep learning tasks
https://doi.org/10.34680/2076-8052.2022.3(128).70-74
Abstract
In order to obtain reasonable practical results of the study of infocommunication systems and communication networks, as well as to put them into practice when solving deep learning problems, the article considers the software implementation of the task of analyzing uniformly and normally distributed random variables. Along with a theoretical analysis, the article presents experimental study results. Uniform and normal distributions are considered. A solution to the problem of transforming a random sample so that it obeys the standard normal distribution is given. The software generates sequences of random variables, which are summed element by element. The problem of calculating the density function, the mean value, and the variance of the sum of two uniformly distributed random variables has been solved. The transformation of a uniform distribution into a normal distribution has been performed. For two independent and uniformly distributed random variables, a two-dimensional density function has been defined. The software implementation has been performed using the Matlab mathematical modeling program. The results of theoretical studies and software implementation are shown in graphs.
About the Author
A. A. Sherstneva
Санкт-Петербургский государственный университета телекоммуникаций им. проф. М.А. Бонч-Бруевича
Russian Federation
Russian Federation
References
1. Eremenko Yeremenko V.T., Fisun A.P., Saitov I.A., et al. Metody i modeli teorii teletrafika: uchebnoe posobie [Methods and models of teletraffic engineering: lecture notes]. Orel, OSU named after I.S. Turgenev Publ., 2019. 244 p.
2. Stepanov S. N. Teoriya teletrafika: kontseptsii, modeli, prilozheniya [Teletraffic engineering: concepts, models, applications]. Moscow, Goryachaya liniya — Telekom Publ., 2015. 868 p.
3. GOST R ISO 28640-2012. Statisticheskie metody. Generatsiya sluchaynykh chisel [Statistical methods. Random variate generation]. 2013. 15 p.
4. GOST P 50779.21-2004. Statisticheskie metody. Pravila opredeleniya i metody rascheta statisticheskikh kharakteristik po vyborochnym dannym [Statistical methods. Rules for determining and methods for calculating statistical characteristics from sample data]. 2004. 47 p.
5. Wasserman L. All of Statistics. New York, Springer Publ., 2004. 433 p.
6. Alizadeh M., Beheshti M.T.H., Ramezani A., Saadinejad H. Network traffic forecasting based on fixed telecommunication data using deep learning. 6th Iranian Conference on Signal Processing and Intelligent Systems (ICSPIS), 2020, pp. 1–7. doi: https://doi.org/10.1109/ICSPIS51611.2020.9349573
7. Kolemaev V.A., Kalinina V.N. Teoriya veroyatnostey i matematicheskaya statistika: uchebnik [Probability Theory and Mathematical Statistics: Textbook]. Moscow, INFRA-M Publ., 1997. 302 p.
8. Guan W., Zhang H., and Leung V.C.M. Analysis of traffic performance on network slicing using complex network theory. IEEE Transactions Technology, 2020, vol. 69, рp. 15188–15199. doi: https://doi.org/10.1109/TVT.2020.3036934
9. Kay S. Intuitive probability and random processes using Matlab. New York, Springer Publ., 2006. 834 p.
10. Dovbnya V.G., Koptev D.S. Matematicheskaya model' priyemnogo trakta tsifrovykh liniy svyazi [Mathematical model of the receiving path of digital communication lines]. T-comm, 2021, no. 5, pp. 52–57.
Review
For citations:
Sherstneva A.A. Software implementation of the analysis of uniformly and normally distributed random variables for deep learning tasks. Title in english. 2022;(3(128)):70-74. (In Russ.) https://doi.org/10.34680/2076-8052.2022.3(128).70-74
Views:
34
Email this article 