Effective Measyrand Estimators for Samples of Trapezoidal PDF-s

• Autorzy: Warsza Z. L.
• Języki publikacji: EN

Abstrakty

EN

This paper is final overview of investigations on the accuracy of basic estimators of trapezoidal probability distribution samples of the measured data. For symmetrical trapezoidal PDF of straight as well concaved sides, using Monte-Carlo method of simulation, the standard deviation (SD) of linear 1- and 2-component estimators are evaluated. Approaches for theirs evaluation are proposed. It is established that in the ratio of upper and bottom bases of trapezoidal PDF in the range from 1 to 0,35 the mid-range value has smaller standard deviation (SD) than the mean value and median. It is find then for the whole family of the symmetric linear trapezoidal PDF more accurate than above single element estimators are two-component (2C) estimators as the linear form of the mean and mid-range values of the sample. Their coefficients are found, properties discussed and formulas of SD are given. The new simplified 2C-estimator of equal coefficients is also proposed. These estimators successfully extend estimation of the measurand value as the sample mean and description of its accuracy by the uncertainty type A recommended by the international guides of uncertainty evaluation in measurement GUM-2008 [1], EA-4/02 [2] and by Handbook NASA [3]. Approaches of described below investigations could be effectively applied also for other models of convoluted PDF-s.

Słowa kluczowe

EN

estimators of probability density function; trapezoidal PDF; mid-range; uncertainty evaluation

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2012
• Tom: Vol. 6, No. 1
• Strony: 8--14
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Warsza Z. L.

• Industrial Institute of Control and Measurement PIAP, Warsaw, Poland,

Bibliografia

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• [3] Measurement Uncertainty Analysis Principles and Methods, NASA Measurement Quality Assurance Handbook –Annex 3, HDBK-8739.19-3, July 2010 Washington DC.
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• [9] Kacker R. N., Lawrence J. F., “Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty” Metrologia, no. 44, 2007, pp. 117–127.
• [10] Warsza Z. L., Galovska M., “About the best measurand estimators of trapezoidal probability distributions”, Przegląd Elektrotechniki (Electrical Review), no. 5, 2009, pp. 86–91.
• [11] Warsza Z. L., Galovska M., “The best measurand estimators of trapezoidal PDF”. In: Proceedings of IMEKO World Congress Fundamental and Applied Metrology, 2009, Lisbon, CD, pp. 2405–2410.
• [12] Galovska M., Warsza Z. L., The ways of effective estimation of measurand”, PAKgoś (Pomiary Automatyka Komputery w gospodarce i ochronie środowiska), no.1, 2010, pp. 18-20.