Share:


Mathematical analysis of synthetic meters based on radar charts

    Boleslaw Borkowski Affiliation
    ; Artur Wiliński   Affiliation
    ; Wieslaw Szczesny Affiliation
    ; Zbigniew Binderman Affiliation

Abstract

This work contains a description of a technique for constructing two synthetic indicators (measures) using a graphical presentation in the form of radar maps. The paper presents the structure and properties of indicators and their formal notation specially created for this purpose using the analogon of a scalar product of vectors. In particular, it proves the theorem on polygon fields, induced by radar maps, prepared for structural vectors, which allows to build concentration indicators. In order to demonstrate the usefulness of tools constructed by such means, the example shows how significant structural changes can be imperceptible when utilizing only the GINI concentration indicator’s value, but are noticeable when using the concentration indicator developed by the authors. In addition, it illustrates the change in the value of concentration indicators (GINI and the indicator developed by the authors) on two families of Lorenz curves, together with changes in concentration. The practical application of this technique for constructing indicators that create rankings is presented on empirical data on the level of material deprivation in the countries that joined the EU in 2004 and 2007. These data have also been annotated (for comparison purposes) using the so-called overrepresentation maps (Grade Correspondence Analysis method).

Keyword : radar chart, concentration meter, S-shift operator

How to Cite
Borkowski, B., Wiliński, A., Szczesny, W., & Binderman, Z. (2020). Mathematical analysis of synthetic meters based on radar charts. Mathematical Modelling and Analysis, 25(3), 473-489. https://doi.org/10.3846/mma.2020.11223
Published in Issue
Jul 8, 2020
Abstract Views
281
PDF Downloads
236
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

R.A. Barnett, M.R. Ziegler, K.E. Byleen and Ch.J. Stocker. College Mathematics for Business, Economics, Life Sciences, and Social Sciences, 10th ed. Pearson Prentice Hall, 2005.

Z. Binderman, B. Borkowski, R. Kozera, A. Prokopenya and W. Szczesny. On mathematical modelling of synthetic measures. Mathematical Modeling and Analysis, 23(4):699–711, 2018. https://doi.org/10.3846/mma.2018.042

Z. Binderman, B. Borkowski and W. Szczesny. Radar coefficient of concentration. Quantitative methods in economics, 13(2):7–21, 2012.

Z. Binderman, W. Szczesny and A. Prokopenya. Radar coefficients of concentrations verifications of properties. Computer Algebra Systems in Teaching and Research, Siedlce, ed. Collegium Mazovia, pp. 16–28, 2013.

I.M. Gelfand. Lectures on linear algebra. New York, Interscience, 1961.

C. Gini. Sulla misura della concentrazione e della variabilità dei caratteri. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. A.A., 73(2):1203–48, 1914.

G.J. Glasser. Variance formulas for the mean difference and coefficient of concentration. Journal of the American Statistical Association, 57(229):648–654, 1962. https://doi.org/10.1080/01621459.1962.10500553

L.D. Hoffmann and G.L. Bradley. Calculus for Business, Economics, and the Social and Life Sciences, 9th ed. McGraw Hill, New York, 2007.

T. Kowalczyk, E. Pleszczyńska and F. Ruland. Grade models and methods for data analysis. Studies in Fuzziness and Soft Computing. Vol. 151. Springer, Berlin, Heidenberg, New York, 2004. https://doi.org/10.1007/978-3-540-39928-5

W. Szczesny. Grade correspondence analysis applied to contingency tables and questionnaire data. Intelligent Data Analysis, 6(1):17–51, 2002. https://doi.org/10.3233/IDA-2002-6103

N.R. Tague. The quality toolbox, second edition. ASQ Quality Press, 2005.

A. Wiliński and S. Osowski. Ensemble of data mining methods for gene ranking. Bulletin of the Polish Academy of Sciences: Technical Sciences, 60(3):461–471, 2012. https://doi.org/10.2478/v10175-012-0058-x

A. Wilinski. Extraction of essential features by quantum density. In R.S. Romaniuk(Ed.), Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2016, volume 10031, pp. 1528–1534. International Society for Optics and Photonics, SPIE, 2016. https://doi.org/10.1117/12.2249406

J.Z. Zawistowski, W. Szczesny, B. Borkowski, R. Kozera and Y. Shachmurove. Alternative method of measuring concentration. Applied Mathematics & Information Sciences, 10(1):11–19, 2016. https://doi.org/10.18576/amis/100102