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 J. Comp. Eng. Math., 2017, Volume 4, Issue 4, Pages 53–63 (Mi jcem105)

Computational Mathematics

Conditions of obtaining the discrete kurtosis spectrum of statistical distributions of biometric data for small samples

V. I. Volchikhina, A. I. Ivanovb, A. I. Gazinc, A. G. Bannykha

a Penza State University, Penza, Russian Federation
b Penza Scientific Research Electrotechnical Institute, Penza, Russian Federation
c Lipetsk State Pedagogical University named after P.P. Semenov-Tyan-Shan, Lipetsk, Russian Federation

Abstract: The aim of the paper is to amplify the statistic criterions in small test samples. We propose to use the simulation tools and numerically get the density of distribution of statistical excess criterion values in small samples. The spectrum of excess criterion states becomes discrete, when the histogram intervals are synchronized with the mathematical expectation of the sample. The chi-square Pearson's molecule constructed before was created with the use of the second-order statistical moment. In this paper, we prove that such constructions are also efficient for forth-order statistical moments. The chi-square mathematical Pearson's molecule and mathematical excess molecule are analogous. We surmise that there are infinitely many mathematical molecules, which are similar to the actual physical molecules in their properties. The Schrödinger equations are not unique; their analogues can be constructed for each mathematical molecule. We can expect a synthesis of the mathematical molecules with inner multidimensional continuum states of "electrons" and their displays in the form of discrete output spectrums of states for sixth-, eighth-order and higher even statistical moments.

Keywords: quantum superposition, chi-square Pearson's criterion, discrete spectrum of states, statistical analysis of small samples.

DOI: https://doi.org/10.14529/jcem170405

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UDC: 519.24, 53, 57.017
MSC: 62P10, 62P35
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Citation: V. I. Volchikhin, A. I. Ivanov, A. I. Gazin, A. G. Bannykh, “Conditions of obtaining the discrete kurtosis spectrum of statistical distributions of biometric data for small samples”, J. Comp. Eng. Math., 4:4 (2017), 53–63

Citation in format AMSBIB
\Bibitem{VolIvaGaz17} \by V.~I.~Volchikhin, A.~I.~Ivanov, A.~I.~Gazin, A.~G.~Bannykh \paper Conditions of obtaining the discrete kurtosis spectrum of statistical distributions of biometric data for small samples \jour J. Comp. Eng. Math. \yr 2017 \vol 4 \issue 4 \pages 53--63 \mathnet{http://mi.mathnet.ru/jcem105} \crossref{https://doi.org/10.14529/jcem170405} \elib{http://elibrary.ru/item.asp?id=30753508}