Abstract
For a measuring instrument, a usual way to find the probability distribution of its measurement errors is to compare its results with the results of measuring the same quantity with a much more accurate instrument. But what if we are interested in estimating the measurement accuracy of a state-of-the-art measuring instrument, for which no more accurate instrument is possible? In this paper, we show that while in general, such estimation is not possible; however, can uniquely determine the corresponding probability distributions if we have several state-of-the-art measuring instruments, and for one of them, the corresponding probability distribution is symmetric.
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References
Bracewell, R.N.: Fourier Transform and Its Applications. McGraw Hill, New York (1978)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge, Massachusetts (2009)
Novitskii, P.V., Zograph, I.A.: Estimating the Measurement Errors. Energoatomizdat, Leningrad (1991). (in Russian)
Ochoa, O., Velasco, A., Servin, C.: Towards model fusion in geophysics: how to estimate accuracy of different models. J. Uncertain Syst. 7(3), 190–197 (2013)
Orfanidis, S.: Introduction to Signal Processing. Prentice Hall, Upper Saddle River, New Jersey (1995)
Orlov, A.I.: How often are the observations normal? Ind. Lab. 57(7), 770–772 (1991)
Rabinovich, S.: Measurement Errors and Uncertainties: Theory and Practice. American Institute of Physics, New York (2005)
Servin, C., Kreinovich, V.: Propagation of Interval and Probabilistic Uncertainty in Cyberinfrastructure-Related Data Processing and Data Fusion. Springer Verlag, Berlin, Heidelberg (2015)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC Press, Boca Raton, Florida (2011)
Sneddon, I.N.: Fourier Transforms. Dover Publisher, New York (2010)
Acknowledgements
This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence).
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Servin, C., Kreinovich, V. (2018). Comparisons of Measurement Results as Constraints on Accuracies of Measuring Instruments: When can we Determine the Accuracies from These Constraints?. In: Ceberio, M., Kreinovich, V. (eds) Constraint Programming and Decision Making: Theory and Applications. Studies in Systems, Decision and Control, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-61753-4_16
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DOI: https://doi.org/10.1007/978-3-319-61753-4_16
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