# Article

 Article title SECOND ORDER HISTOGRAM FOR NUMERICAL SIMULATION PROBLEMS WITH INFORMATION UNCERTAINTY Authors O.A. Popova Section SECTION I. MODELING OF SYSTEMS AND PROCESSES Month, Year 06, 2014 @en Index UDC 519.24 DOI Abstract The solution of many practical problems with information uncertainty of input data requires special techniques based on the submission procedures and numerical simulation. The article describes the uncertainty propagation procedures (propagation of uncertainty) and an analysis of existing methods of its representation. To solve such problems are encouraged to use numerical probabilistic analysis. Numerical probabilistic analysis is a way for propagation of information uncertainty, including problems when probabilistic estimates of the input parameters are uncertain. To reduce the level of information uncertainty and to have more information about the distribution of the parameters in an information insufficiency is proposed to use the histogram approach. Representation of uncertainty contained in the input data is performed using a secondorder histograms, which are constructed on the basis of its distribution procedures. For this purpose, based on a second order histogram is developed the arithmetic of undefined data. There are numerical examples and discussing the practical applications. Download PDF Keywords Information uncertainty; uncertainty propagation procedures; numerical probabilistic analysis; second order histogram. References 1. Ferson S., Ginzburg L. Different methods are needed to propagate ignorance and Variability // Reliability Engineering and System Safety. – 1996. – № 54. – C. 133-144. 2. Neumaier A. Clouds, Fuzzy Sets and Probability Intervals // Reliable Computing. – 2004. – № 10. – С. 249-272. 3. Dempster A.P. Upper and lower probabilities induced by a multi-valued mapping // Annals of Mathematical Statistics. – 1967. – № 38. – C. 325-339. 4. Dobronets B.S., Krantsevich A.M., Krantsevich N.M. Software implementation of numerical operations on random variables // Journal of Siberian Federal University. Mathematics & Physics. – 2013. – № 6 (2). – C. 168-173. 5. Skyrms B. Higher Order Degrees of Belief // Prospects for Pragmatism: Essays in Memory of F.P. Ramsey, D.H. Mellor, ed. Cambridge; New York: Cambridge University Press. – 1980. – Р. 109-137. 6. Попова О.А. Технология извлечения и визуализации знаний на основе численного вероятностного анализа неопределенных данных // Информатизация и связь, – 2013. – № 2. – С. 63-66. 7. Popova O.A. Optimization problems with random data // Journal of Siberian Federal University. Mathematics & Physics. – 2013. – № 6 (4). – C. 506-515.