Abstract
A procedure for the determining of the measure of non-gaussianity of nearly Gaussian noise is suggested, which used trimmed interval of concentration. The procedure is based on the Parseval finite-interval theorem. The following notions have been introduced: the scalar measure of non-gaussianity, the vector measure of non-gaussianity, and multicomponent partial measure of non-gaussianity. The method allows decreasing the probability of the mistaking of a purely Gaussian noise for nearly Gaussian one. The procedure was validated using a mixed normal distribution. The testing showed the finite-interval analog of the Gram-Charlier expansion to have only a few main (meaningful) components. The procedure for the determining of the measure of non-gaussianity of nearly Gaussian noise can be used in the noise diagnostics of various electrochemical systems and for noise monitoring of objects and processes in the electrochemical power engineering.
This is a preview of subscription content, log in via an institution to check access.
References
Vandamme, L.K.J., IEEE Transactions Electron Device, 1994, vol. 41, p. 2176.
Ciofi, C. and Neri, B., J. Physics D: Applied Physics, 2000, vol. 33, p. R199.
Jones, B.K., IEE Proceedings-Circuits, Devices, 2002, vol. 149, p. 13.
Mansfeld, F., Electrochim. Acta, 2001, vol. 46, p. 3651.
Huet, F., Musiani, M., and Nogueira, R.P., Electrochim. Acta, 2003, vol. 48, p. 3981.
Lafront, A.-M., Ghali, E., and Morales, A.T., Electrochim. Acta, 2007, vol. 52, p. 5076.
Cottis, R.A., Electrochim. Acta, 2007, vol. 52, p. 7585.
Timashev, S.F. and Polyakov, Yu.S., Fluctuation Noise Letters, 2007, vol. 7, p. R15.
Legros, B., Thivel, P.-X., Bultel, Y., and Nogueira, R.P., Electrochem. Commun., 2011, vol. 13, p. 1514.
Cramer, H., Mathematical Methods of Statistics, Princeton, 1954.
Arley, N. and Buch, K.R., Introduction to the Theory of Probability and Statistics, New York, 1950.
Hudson, D.J, Statistics. Lectures on Elementary Statistics and Probability, Geneva, 1964.
Levin, B.R., Teoreticheskie osnovy statisticheskoi radiotekhniki (Theory of Statistical Radio Engineering), Moscow: Sov. Radio, 1975.
Wilcox, R.R., Fundamentals of Modern Statistical Methods, New York: Springer, 2010.
Aivazian, S.A. and Mkhitarian, V.S., Applied Statistics and Essentials of Econometrics, Moscow: UNITY, 1998.
Kendall, M.G. and Stuart, A., The Advanced Theory of Statistics, vol. 2, London: Charles Griffin, 1961.
Patil, G.P., Weighted Distributions. Encyclopedia of Environments, vol. 4, El-Shaarawi, A.H. and Piegorsch, W.W., Eds., Chichester: Wiley, 2002, p. 2369.
Kampe de Feriet, J., Vogel, Th., Petiau, G., and Campbell, R., Fonctions de la physique mathematique, CNRS, 1957.
Puuronen, J. and Hyvarinen, A., Lect. Notes Comp. Sci., 2011, vol. 6792/2011, p. 205.
Blinnikov, S. and Moessner, R., Astronomy Astrophysics, Suppl. Series, 1998, vol. 130, p. 193.
Stratonovich, R.L., Topics in the Theory of Random Noise, New-York: Gordon and Breach, 1963.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © B.M. Grafov, 2014, published in Elektrokhimiya, 2014, Vol. 50, No. 5, pp. 548–553.
Rights and permissions
About this article
Cite this article
Grafov, B.M. On the measure of non-gaussianity of a nearly Gaussian noise. Russ J Electrochem 50, 490–495 (2014). https://doi.org/10.1134/S1023193514050061
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1023193514050061