Treatment of Experimental Data with Discordant Observations: Issues in Empirical Identification of Distribution

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Treatment of Experimental Data with Discordant Observations: Issues in Empirical Identification of Distribution

Performances of several methods currently used for detection of discordant observations are reviewed, considering a set of absolute measurements of gravity acceleration exhibiting some peculiar features. Along with currently used methods, a criterion based upon distribution of extremes is also relied upon to provide references; a modification of a simple, broadly used method is mentioned, improving performances while retaining inherent ease of use. Identification of distributions underlying experimental data may entail a substantial uncertainty component, particularly when sample size is small, and no mechanistic models are available. A pragmatic approach is described, providing estimation to a first approximation of overall uncertainty, covering both estimation of parameters, and identification of distribution shape.

Barnett, V., Lewis, T. (1978). The study of outliers: Purpose and model. Applied Statistics, 27, 242-250.

Barnett, V., Lewis, T. (1994). Outliers in Statistical Data (3rd ed.). New York, USA: Wiley.

Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM). JCGM 100:2008. Sèvres, France.

Zakrzewski, J. (2003). Error and uncertainty reduction - challenge for a measuring systems designer. Measurement Science Review, 3 (1), 31-34.

Song, J., Vorburger, T., Thompson, R., Renegar, T., Zheng, A., Ma, L., Yen, J., Ols, M. (2010). Three Steps towards metrological traceability for ballistics signature measurements. Measurement Science Review, 10 (1), 19-21.

Rhind, A. (1909). Tables to facilitate the computation of the probable errors of the chief constants of skew frequency distributions. Biometrika, 7 (1/2), 127-147.

Hahn, G. J., Shapiro, S. S. (1967). Statistical Models in Engineering. New York, USA: Wiley.

Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36 (1/2), 149-176.

Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. Philosophical Transactions of the Royal Society of London A, 186, 343-414.

D'Agostino, G. (2005). Development and metrological characterization of a new transportable absolute gravimeter. Unpublished Doctoral Dissertation, Politecnico di Torino, Torino, Italy.

Niebauer, T. M., Sasagawa, G. S., Faller, J. E., Hilt, R., Klopping, F. (1995). A new generation of absolute gravimeters. Metrologia, 32 (3), 159-180.

Bich, W., D'Agostino, G., Germak, A., Pennecchi, F. (2008). Reconstruction of the free- falling body trajectory in a rise-and-fall absolute ballistic gravimeter. Metrologia, 45 (3), 308-312.

Hanada, H., Tsubokawa, T., Tsuruta, S. (1996). Possible large systematic error source in absolute gravimetry. Metrologia, 33 (2), 155-160.

Bich, W., D'Agostino, G., Pennecchi, F., Germak, A. (2011). Uncertainty due to parasitic accelerations in absolute gravimetry. Metrologia, 48 (3), 212-218.

Gumbel, E. J. (1958). Statistics of Extremes. New York, USA: Columbia University Press.

Barbato, G., Barini, E. M., Genta, G., Levi, R. (2011). Features and performance of some outlier detection methods. Journal of Applied Statistics, 38 (10), 2133-2149.

David, H. A., Nagaraja, H. N. (2003). Order Statistics (3rd ed.). New York, USA: Wiley.

Kendall, M. G., Stuart, A. (1977). The Advanced Theory of Statistics (4th ed.). London, UK: Griffin.

Ord, J. K. (1968). The discrete Student's t distribution. The Annals of Mathematical Statistics, 39 (5), 1513-1516.

Natrella, M. G. (1963). Experimental Statistics. NBS Handbook 91. Washington, USA: National Bureau of Standards.

Hill, I. D., Hill R., Holder R. L. (1976). Algorithm AS99: Fitting Johnson curves by moments. Applied Statistics, 25, 180-189.

DeBrota, D. J., Dittus R. S., Roberts, S. D., Wilson, J. R. (1989). Visual interactive fitting of bounded Johnson distributions. Simulation, 52, 199-205.

Gumbel, E. J. (1960). Discussion of the papers of Messrs. Anscombe and Daniel. Technometrics, 2 (2), 165-166.

Genta, G. (2010). Methods for Uncertainty Evaluation in Measurement. Saarbrücken, Germany: VDM Verlag.

Youden, W. J. (1972). Enduring values. Technometrics, 14 (1), 1-11.

Measurement Science Review

The Journal of Institute of Measurement Science of Slovak Academy of Sciences

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