ГОСТ Р 54500.3.1-2011/Руководство ИСО/МЭК 98-3:2008/Дополнение 1:2008 Неопределенность измерения. Часть 3. Руководство по выражению неопределенности измерения. Дополнение 1. Трансформирование распределений с использованием метода Монте-Карло

[1]

Beatty, R.W. Insertion loss concepts. Proc. IEEE 52, 1964, pp.663-671

[2]

Berthouex, P.M. and Brown, L.C. Statistics for Environmental Engineers. CRC Press, USA, 1994

[3]

Box, G. E. P. and Muller, M. A note on the generation of random normal variates. Ann. Math. Statist., 29, 1958, pp.610-611

[4]

Chan, A., Golub, G. and Leveque, R. Algorithms for computing the sample variance: analysis and recommendations. Amer. Stat., 37, 1983, pp.242-247

[5]

Conte, S.D. and De Boor, С. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill, 1972

[6]

Cox, M.G. The numerical evaluation of B-splines. J. Inst. Math. Appl. 10, 1972, pp.134-149

[7]

Cox, M.G. and Harris, P.M. Software specifications for uncertainty evaluation. Tech. Rep. DEM-ES-010, National Physical Laboratory, Teddington, UK, 2006

[8]

Cox, M.G. and Harris, P.M. SSfM Best Practice Guide No. 6, Uncertainty evaluation. Tech. Rep. DEM-ES-011, National Physical Laboratory, Teddington, UK, 2006

[9]

Cox, M.G. and Siebert, B. R. L. The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia, 43, 2006, pp.S178-S188

[10]

David, H.A. Order Statistics. Wiley, New York, 1981

[11]

Dekker, T.J. Finding a zero by means of successive linear interpolation. In: Constructive Aspects of the Fundamental Theorem of Algebra (eds Dejon B. and Henrici P.), Wiley Interscience, London, 1969

[12]

Devroye, L. Non-Uniform Random Number Generation. Springer, New York, 1986

[13]

Dietrich, C.F. Uncertainty, Calibration and Probability. Adam Hilger, Bristol, UK, 1991

[14]

Dowson, D.C. and Wragg, A. Maximum entropy distributions having prescribed first and second order moments. IEEE Trans. IT, 19, 1973, pp.689-693

[15]

EA. Expression of the uncertainty of measurement in calibration. Tech. Rep. EA-4/02, European Cooperation for Accreditation, 1999

[16]

Elster, С. Calculation of uncertainty in the presence of prior knowledge. Metrologia, 44, 2007, pp.111-116

[17]

EURACHEM/CITAC. Quantifying uncertainty in analytical measurement. Tech. Rep. Guide CG4, EURACHEM/CITEC, 2000. Second edition

[18]

Evans, M., Hastings, N. and Peacock, B. Statistical distributions. Wiley, 2000

[19]

FRENKEL, R.B. Statistical background to the ISO 'Guide to the Expression of Uncertainty in Measurement'. Tech. Rep. Monograph 2, NML Technology Transfer Series, Publication number TIP P1242, National Measurement Laboratory, CSIRO, Australia, 2002

[20]

Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis. Chapman and Hall, London, 2004

[21]

Gleser, L.J. Assessing uncertainty in measurement. Stat. Sci., 13, 1998, pp.277-290

[22]

Hall, B.D. and Willink, R. Does "Welch-Satterthwaite" make a good uncertainty estimate? Metrologia, 38, 2001, pp.9-15

[23]

Higham, N.J. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 1996

[24]

ISO 3534-1:19932) Statistics - Vocabulary and symbols - Part 1: Probability and general statistical terms

[25]

Jaynes, E. T. Information theory and statistical mechanics. Phys. Rev, 106, 1957, pp.620-630

[26]

Jaynes, E.T. Where do we stand on maximum entropy? In Papers on Probability, Statistics, and Statistical Physics (Dordrecht, The Netherlands, 1989), R. D. Rosenkrantz, Ed., Kluwer Academic, pp.210-314. http://bayes.wustl.edu/ etj/articles/stand.on.entropy.pdf

[27]

Kacker, R. and Jones, A. On use of Bayesian statistics to make the Guide to the Expression of Uncertainty in Measurement consistent. Metrologia, 40, 2003, pp.235-248

[28]

Kerns, D.M. and Beatty, R.W. Basic Theory of Waveguide Junctions and Introductory Microwave Network Analysis. Pergamon Press, London, 1967

[29]

Kinderman, A., Monahan, J. and Ramage, J. Computer methods for sampling from Student's t-distribution. Math. Comput, 31, 1977, pp.1009-1018

[30]

L'Ecuyer, P. and Simarf, R. TestU01: A software library in ANSI С for empirical testing of random number generators. http://www.iro.umontreal.ca/~simardr/testu01/tu01.html

[31]

Leydold, J. Automatic sampling with the ratio-of-uniforms method. ACM Trans. Math. Software, 26, 2000, pp.78-98

[32]

Lira, I. Evaluating the Uncertainty of Measurement. Fundamentals and Practical Guidance. Institute of Physics, Bristol, UK, 2002

[33]

Lira, I.H. and Woger, W. Bayesian evaluation of the standard uncertainty and coverage probability in a simple measurement model. Meas. Sci. Technol., 12, 2001, pp.1172-1179

[34]

Matsumoto, M. and Nishimura, T. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Modeling and Computer Simulation 8 (1998), pp.3-30

[35]

McCullough, B.D. and Wilson, B. On the accuracy of statistical procedures in Microsoft Excel 2003. Computational Statistics and Data Analysis, 2004

[36]

Moler, C.B. Numerical computing with MATLAB. SIAM, Philadelphia, 2004

[37]

NETLIB. The Netlib repository of freely available software, documents, and databases of interest to the numerical, scientific computing, and other communities contains facilities for sampling from probability distributions, http://www.netlib.org

[38]

NIST. The NIST Digital Library of Mathematical Functions contains facilities for sampling from probability distributions, http://dlmf.nist.gov

[39]

OIML. Conventional value of the result of weighing in air. Tech. Rep. OIML D 28, Organisation Internationale de Metrologie Legale, Paris, 2004

[40]

Papoulis, A. On an extension of Price's theorem. IEEE Trans. Inform. Theory IT-11, 1965

[41]

Price, R. A useful theorem for nonlinear devices having Gaussian inputs. IEEE Trans. Inform. Theory IT-4, 1958, pp.69-72

[42]

Rice, J. R. Mathematical Statistics and Data Analysis, second ed. Duxbury Press, Belmont, Ca., USA, 1995

[43]

Ridler, N.M. and Salter, M.J. Propagating S-parameter uncertainties to other measurement quantities. In: 58th ARFTG (Automatic RF Techniques Group) Conference Digest (2001)

[44]

Robert, C.P. and Casella, G. Monte Carlo Statistical Methods. Springer-Verlag, New York, 1999

[45]

Salter, M.J., Ridler, N.M. and Cox, M.G. Distribution of correlation coefficient for samples taken from a bivariate normal distribution. Tech. Rep. CETM 22, National Physical Laboratory, Teddington, UK, 2000

[46]

Schoenberg, I.J. Cardinal interpolation and spline functions. J. Approx. Theory, 2, 1969, pp.167-206

[47]

Scowen, R.S. Algorithm 271: quickersort. Communications of the ACM, 8(11), 1965, pp.669-670

[48]

Shannon, C.E. A mathematical theory of information. Bell Systems Tech. J., 27, 1948, pp.623-656

[49]

Strang, G. and Borre, K. Linear Algebra, Geodesy and GPS. Wiley, Wellesley-Cambridge Press, 1997

[50]

Taylor, B.N. and Kuyatt, C.E. Guidelines for evaluating and expressing the uncertainty of NIST measurement results. Tech. Rep. TN1297, National Institute of Standards and Technology, USA, 1994

[51]

Weise, K., and Woger, W. A Bayesian theory of measurement uncertainty. Meas. Sci. Technol., 3, 1992, pp.1-11

[52]

Wichmann, B.A. and Hill, I.D. Algorithm AS183. An efficient and portable pseudo-random number generator. Appl. Statist., 31, 1982, pp.188-190

[53]

Wichmann, B.A. and Hill, I.D. Correction. Algorithm AS183. An efficient and portable pseudo-random number generator. Appl. Statist., 33, 1984, p.123

[54]

Wichmann, B.A. and Hill, I.D. Generating good pseudo-random numbers. Computational Statistics and Data Analysis, 51, 2006, pp.1614-1622

[55]

Willink, R. Coverage intervals and statistical coverage intervals. Metrologia, 41, 2004, L5-L6

[56]

Woger, W. Probability assignment to systematic deviations by the Principle of Maximum Entropy. IEEE Trans. Instr. Measurement IM-36, 1987, pp.655-658