Estimation of random variable distribution parameters by the monte carlo method

• Autorzy: Sienkowski S.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.

Słowa kluczowe

EN

Monte Carlo method; mean; mean square; variance

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2013
• Tom: Vol. 20, nr 2
• Strony: 249--262
• Opis fizyczny: Bibliogr. 34 poz., wykr., wzory

Twórcy

autor

Sienkowski S.

• University of Zielona Góra, Faculty of Electrical Engineering, Computer Science and Telecommunication, Institute of Electrical Metrology, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] Evaluation of measurement data. (2008). Guide to the expression of uncertainty in measurement, JCGM 100, GUM 1995.
• [2] Evaluation of measurement data. (2008). Supplement 1 to the "Guide to the expression in measurement" - Propagation of distributions using a Monte Carlo method, JCGM 101.
• [3] Evaluation of measurement data. (2011). Supplement 2 to the "Guide to the expression of uncertainty in measurement" - Extension to any number of output quantities, JCGM 102.
• [4] Krajewski, M. (2012). Construction of uncertainty budget using the Monte Carlo method for analysis of digital signal algorithm properties. Measurement Automation and Monitoring, 9, 770-773.
• [5] Couto, P.R.G, Damasceno, J.C., et al. (2009). Comparative analysis of the measurement uncertainty of the deformation coefficient of a pressure balance using the GUM approach and Monte Carlo simulation methods. XIX IMEKO World Congress: Fundamental and Applied Metrology, 2051-2054.
• [6] Fraga, I. C. S., Couto, P. R. G., et al. (2008). Uncertainty budget for primary electrolytic conductivity measurement comparing different methods. 2nd IMEKO TC19: Conference on environmental measurements, 1st IMEKO TC23: Conference on food and nutritional measurements.
• [7] Kovacevič , A., Kovacevič , D., Osmokrovič , P. (2012). Uncertainty evaluation of conducted emission measurement by the Monte Carlo method and the modified least-squares method. Progress in electromagnetics research symposium proceedings, 1173-1179.
• [8] Cox, M. G., Siebert, B. R. L. (2006). The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia, 43, 178-188.
• [9] Wübbeler, G., Krystek, M., Elster, C. (2008). Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method. Measurement science and technology, 19(8), 084009.
• [10] Kreutzer, Ph., Dorozhovets, N., et al. (2009). Monte Carlo simulation to determine the measurement uncertainty of a metrological scanning probe microscope measurement. SPIEInternational Society for Optical Engineering, 7378, 737816-737816-12.
• [11] Lal-Jadziak, J., Sienkowski, S. (2008). Models of bias of mean square value digital estimator for selected deterministic and random signals, Metrology and Measurement Systems, 15(1), 55-69.
• [12] Lal-Jadziak, J., Sienkowski, S. (2009). Variance of random signal mean square value digital estimator, Metrology and Measurement Systems, 16(2), 267-278.
• [13] Hammersley, J.M., Handscomb, D.C. (1964). Monte Carlo methods. London: Methuen & Co.
• [14] Buslenko, N.P., Golenko, D.I., et al. (1967). The Monte Carlo method. International series of monographs in pure and applied mathematics, 87, Pergamon Press, Oxford.
• [15] Zieliński, R. (1970). Monte Carlo methods. Polish Scientific and Technical Publishers.
• [16] Jermakow, S.M. (1976). Monte Carlo method and related problems. Polish Scientific Publishers.
• [17] Jain, S. (1992). Monte Carlo simulations of disordered system. World Scientific Publishing Company.
• [18] Fishman, G.S. (2003). Monte Carlo concepts, algorithms, and applications. Springer-Verlag, New York.
• [19] Gentle, J.E. (2005). Random number generation and Monte Carlo methods. Springer Science+Business Media.
• [20] Dagpunar, J. S. (2007). Simulation and Monte Carlo with applications in finance and MCMC. John Wiley & Sons.
• [21] Kalos, M.H., Whitlock, P.A. (2008). Monte Carlo Methods. John Wiley & Sons.
• [22] Rubinstein, R.Y., Kroese, D.P. (2008). Simulation and the Monte Carlo method. John Wiley & Sons.
• [23] Shlomo, M., Shaul, M. (2009). Applications of Monte Carlo method in science and engineering. Cambridge University Press.
• [24] Landau, D. P., Binder, K. (2009). A guide to Monte Carlo simulations in statistical physics. Cambridge University Press.
• [25] Dunn, W.L., Shultis, J.K. (2012). Exploring Monte Carlo methods. Elsevier B.V.
• [26] Sienkowski, S. (2012). Estimation of random variable distribution parameters by Monte Carlo method. Computer program: http://www.ime.uz.zgora.pl/ssienkowski/apps/soft/imemc.rar. Web page: http://www.ime.uz.zgora.pl/ssienkowski/imemc.html.
• [27] Papoulis, A., Pillai, S. U. (2002). Probability, random variables, and stochastic processes. New York: McGraw-Hill.
• [28] Wikramaratna, R. (2000). Pseudo-random number generation for parallel Monte Carlo - a splitting approach. Society for Industrial and Applied Mathematics News, 33(9).
• [29] Mohanty, S., Mohanty, A. K., Carminati, F. (2012). Efficient pseudo-random number generation for Monte-Carlo simulations using graphic processors. Journal of Physics: Conference Series, conference 1, 368(012024).
• [30] Coddinton, P. D. (1994). Analysis of random number generators using Monte Carlo simulation. International Journal of Modern Physics C, 5(3), 547-560.
• [31] National Instruments Corporation. (2012). Web page: http://zone.ni.com/reference/en-XX/help/371361J-01/lvanls/gaussian_white_noise.
• [32] Korn, G. T. (2000). Mathematical handbook for scientists and engineers. New York: McGraw-Hill.
• [33] Liptak, B. G. (2005). Instrument engineer’s handbook: process control and optimization Vol.IV. New York: Taylor and Francis Group.
• [34] Kacker, R.N., Lawrence, J.F. (2007), Trapezoidal and triangular distributions for type B evaluation of standard uncertainty, Metrologia, 44(2), 117-127.