Monte Carlo Method Application and Generation of Random Numbers by Usage of Numerical Methods

  • Dušan Knežo
  • Alena VagaskáEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)


Social scientists increasingly use statistical simulation techniques to help them understand the social processes they care about and the statistical methods used to study them. There are two types of computer simulation techniques, which are quickly becoming essential tools for empirical social scientists: Monte Carlo simulation and resampling methods. This chapter is dealing with Monte Carlo method that is very often used for simulating systems with many coupled degrees of freedom, for simulation of experiments in many areas of research, for investigation of processes with a random character and is most useful when it is difficult to use other approaches. The chapter presents some methods of generating random numbers by usage of standard numerical methods for various probability distributions types as well as application possibility of Monte Carlo method for a CA-simulation of the random processes.


Monte carlo method Random numbers Numerical methods 



The work presented in this chapter has been supported by the project KEGA 026TUKE-4/2016.


  1. Čičmanec, L., Bořil, J.: Assessment of tactical mission simulation exercise. In: Transport Means 2017. Kaunas University of Technology, Kaunas, pp. 729–734 (2017). ISSN 1822-296XGoogle Scholar
  2. Dagpunar, J.S.: Simulation and Monte Carlo: with applications in finance and MCMC. Wiley, ACCEM (2008), New York, (2007), 348 p. ISBN 978-0-470-85494-5Google Scholar
  3. Fishman, G.S.: Monte Carlo Concepts, Algorithms and Applications. Springer, Berlin (1996)zbMATHGoogle Scholar
  4. Gentle, J.E.: Random Number Generation and Monte Carlo Methods. Springer, Berlin (2003)Google Scholar
  5. Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, Berlin (2003)CrossRefGoogle Scholar
  6. Hubacek, M., Vrab, V.: Cost assessment of training using constructive simulation. eBook: Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences, vol. 104. Springer International Publishing AG, New York (2017). ISSN 2198-4182CrossRefGoogle Scholar
  7. Jirgl, M., Bořil, J., Jalovecký, R.: Assessing quality of pilot training with use of mathematical analyses. In: Proceedings of the 2016 17th International Conference on Mechatronics - Mechatronika (ME), Czech Technical University in Prague, Prague, pp. 91–96 (2016). ISBN 978-80-01-05882-4Google Scholar
  8. Knežo, D.: About the method of Monte Carlo and its applications. Transf. Innov. 24, 178–181 (2012a)Google Scholar
  9. Knežo, D.: Estimation of costs concerning prothetic and orthotic aids using the Monte Carlo method. In: AEI’2012: International Conference on Applied Electrical Engineering and Informatics (2012b)Google Scholar
  10. Knežo, D.: Inverse transformation method for normal distribution and the standard numerical methods. Int. J. Interdiscip. Theory Pract. 5(2014), 6–10 (2014)Google Scholar
  11. Kubíček, P., Šašinka, Č., Stachoň, Z.: Selected cognitive issues of positional uncertainty in geographical data. Geografie - Sborník České geografické společnosti, Česká geografická společnost 119(1), 67–90 (2014). ISSN 1212-0014Google Scholar
  12. McLeish, D.L.: Monte Carlo Simulation and Finance. Wiley, New York (2005)Google Scholar
  13. Sobol, I.M.: Die Monte-Carlo-Methode. VEB Deutscher Verlag der Wissenschaften, Berlin (1971)zbMATHGoogle Scholar
  14. Svatoňová, H., Šikl, R.: Cognitive aspects of interpretation of image data. eBook: Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences, vol. 104. Springer International Publishing AG, New York (2017) ISSN 2198-4182CrossRefGoogle Scholar
  15. Urban, R., Hošková-Mayerová, Š.: Threat life cycle and its dynamics. Deturope 9(2), 93–109 (2017)Google Scholar
  16. Woch, M., Zieja, M.,Tomaszewska, J.: Analysis of the time between failures of aircrafts. In: 2nd International Conference on System Reliability and Science (ICSRS 2017), pp. 112–118 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Manufacturing Technologies, Department of Natural Sciences and HumanitiesPrešovSlovak Republic

Personalised recommendations