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Value measurement in statistically uncertain conditions

I. I. Gorban


A mathematical model for measuring values has been proposed taking into account the uncertainty of statistical conditions of forming the measured value and its estimate. This model is based on presenting measured value and its estimate as hyper-random values. The point and interval methods of estimating hyper-random values have been developed. The notions of biased, consistent and efficient estimates were extended to the case of hyper-random estimates. The potential accuracy of measurements was investigated. It was shown that under the conditions of statistically uncertain conditions the potential accuracy of value measurement was limited and determined by the parameters of estimate bias.

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I. I. Gorban, “Hyper-Random Phenomena and Their Description,” Akustychnyi Visnyk 8, Nos. 1–2, 16 (2005).

I. I. Gorban, “The Hyperrandom Functions and Their Description,” Radioelectron. Commun. Syst. 49(1), 1 (2006).

I. I. Gorban, The Theory of Hyper-Random Phenomena (IPMMS NAN Ukrainy, Kyiv, 2007) [in Russian].

I. I. Gorban, “Point and Interval Methods of Estimating Parameters of Hyper-Random Values,” Matematicheskie Mashiny i Sistemy, No. 2, 3 (2006).

Voshchinin, A. F. Bochkov, and G. R. Sotirov, “Data Analysis Method in the Case of Interval Nonstatistical Error,” Zavodskaya Laboratoriya 56, No. 7, 76 (1990).

G. Alefel’d and Yu. Hertsberger, Introduction to Interval Computations (Mir, Moscow, 1987) [in Russian].

V. I. Levin, “Interval Mathematics and the Study of Uncertain Systems,” Informatsionnye Tekhnologii, No. 6(1998) (

I. I. Gorban, “Representation of Physical Phenomena with the Help of Hyper-Random Models,” Matematicheskie Mashiny i Sistemy, No. 1 (2007).

I. I. Gorban, “Mathematical Description of Physical Phenomena in Statistically Unstable Conditions,” Standartyzatsiya, Sertyfikatsiya, Yakist’, No. 6, 26 (2006).

V. S. Korolyuk, et al., Reference Book on the Probability Theory and Mathematical Statistics (Nauka, Moscow, 1985) [in Russian].

I. I. Gorban, Probability Theory and Mathematical Statistics for Researchers and Engineers (IPMMS NAN Ukrainy, Kyiv, 2003) [in Ukrainian].

I. I. Gorban, “Estimates of Characteristics of Hyper-Random Values,” Matematicheskie Mashiny i Sistemy, No. 1, 41 (2006).

B. R. Levin, Theoretical Principles of Statistical Radio Engineering (Radio i Svyaz’, Moscow, 1989) [in Russian].

Van Tris, Theory of Detection, Estimation and Modulation, Vol. 1 (Sov. Radio, Moscow, 1972) [in Russian].

A. I. Orlov, Econometrics. Textbook (Ekzamen, Moscow, 2002) [in Russian].

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