RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Comp. Eng. Math.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (1388 kB)
References: PDF file   HTML file

UDC: 519.24, 53, 57.017
MSC: 62P10, 62P35
Received: 31.10.2017
Language:

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}


Linking options:
  • http://mi.mathnet.ru/eng/jcem105
  • http://mi.mathnet.ru/eng/jcem/v4/i4/p53

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Journal of Computational and Engineering Mathematics
    Number of views:
    This page:55
    Full text:40
    References:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019