Abstract
A statistical infrastructure based on the concentration measures is presented. It aims at being a consistent system of descriptive parameters with a clear interpretation, summarizing knowledge on distributions of variables in populations of objects. The system requires unified formulas for sets of mixed continuous-categorical variables. These demands are met e.g. by the formulas given in Sec. 3 for the bivariate dependence measures, presented as suitably weighted averages of concentration indices for pairs of conditional distributions. Further, in Sec. 4, a concentration oriented modification of the statistical procedure called correspondence analysis is mentioned and exemplified by applying it to data from the Polish Parliament Elections in 1993 and 1997. Sec. 5 contains remarks on creating an inference and computing system adjusted to this new concentration - based approach to statistical descriptive parameters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agresti, A. Analysis of ordinal categorical data. (1990) Wiley, N. York.
Bondarczuk, B., Kowalczyk, T., Pleszczyńska, E., Szczesny, W.: Evaluating departures from fair representation. Applied Stochastic Models and Data Analysis 10 (1994) 169–185.
Cifarelli, D. M., Regazzini, E.: On a general definition of concentration function. Snakhya B 49 (19987) 307–319.
Ciok, A.: Discretization as a tool in cluster analysis. Sixth Conference of the International Federation of Classification Societies, Rome, July 21–24, 1998.
Ciok, A., Kowalczyk, T., Pleszczyńska, E., Szczesny, W.: Algorithms of grade correspondence-cluster analysis. The Collected Papers of Theoretical and Applied Computer Science 7 (1995) 5–22.
Ciok, A., Kowalczyk, T., Pleszczyńska, E., Szczesny, W.: Inequality measures in data analysis. The Collected Papers of Theoretical and Applied Computer Science 6 (1994) 3–20.
Ciok, A.: Generating random MxK tables when row and column totals and cell ranges are given. ICS PAS Reports, No 844 (1997).
Ciok, A.: A comparative study of exploratory methods applied to car switching data. Bulletin of the Polish Academy of Sciences-Technical Sciences (1998).
Ciok, A., Bulhak, W., Skoczylas, R.: Exploration of controlexperimental data by means of grade corresponding analysis. Biocybernetics and Biomedical Engineering 17 (1997).
Ciok, A., Kowalczyk, T., Pleszczyńska, E., Szczesny, W. On comparing departures from proportionality with application to the Polish parliament elections of 1991 and 1993. In: R. Dutter and W. Grossmann (eds.), Short Communications in Computational Statistics (1994) 223–224.
Ciok, A., Kowalczyk, T., Pleszczyńska, E., Szczesny, W.: On a system of grade dependence measures. ICS PAS Reports (1994) No 741.
Fogelson, S.: Measures of concentration and their applications (in Polish), Kwart. Statyst. 10 (1933) 149–197.
Kowalczyk, T.: A unified Lorenz-type approach to divergence and dependence, Dissert. Math. CCXXXV (1994) 1–54.
Kowalczyk, T., Ciok, A., Pleszczyńska, E., Szczesny, W.: Grade dependence in bivariate mixed data: a uniform approach based on concentration curves, submitted (also ICS PAS Reports (1996) No 815).
Kowalczyk, T.: Link between grade measures of dependence and of separability in pairs of conditional distributions, submitted (also ICS PAS Reports (1998) No 849).
Kowalczyk, T.: Decomposition of the concentration index and its implications for the Gini Inequality and Dependence Measures (submitted).
Kowalczyk, T.: Properties of the standard concepts of monotone dependence based on separation curves. Discussiones Mathematicae-Algebra and Stochastic Methods (1997) (to appear).
Kowalczyk, T., Niewiadomska-Bugaj, M.: Grade correspondence analysis based on Kendall’s tau. Sixth Conference of the International Federation of Classification Societies, Rome, July 21–24, 1998.
Pleszczyńska, E., Ciok, A., Kowalczyk, T., Szczesny, W.: New tools of statistical data analysis. Biocybernetics and Biomedical Engineering 15 (1995) 121–137.
Pleszczyńska, E., Ciok, A., Kowalczyk, T.: On parameter decomposition in statistical data analysis. Intelligent Information Systems VI (1997) Proceedings of the Workshop held in Zakopane, Poland, 9–13 June, 1997, 74–85.
Szczesny, W.: On the Performance of a Discriminant Function. J. Classif. 8 (1991) 201–215.
Szczesny, W., Pleszczyńska, E.: A grade statistics approach to exploratory analysis of the HSV data. Biocybernetics and Biomedical Engineering 17 (1997).
Szczesny, W., Grabowski, T., Ciok, A., Kowalczyk, T., Pleszczyńska, E.: A mixed-data grade dependence system and its applications in selection and clustering. In: R. Dutter and W. Grossmann (eds.), COMPSTAT’94, Short Communications in Computational Statistics (1994) 53–54.
Szczesny, W., Ciok, A., Kowalczyk, T., Pleszczyńska, E., Wysocki, W.: A statistical comparative study of 1993 and 1997 Elections to the Polish Parliament (in Polish). ICS PAS Reports (1998) No 851.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ciok, A., Kowalczyk, T., Pleszczyńska, E. (1998). How a New Statistical Infrastructure Induced a New Computing Trend in Data Analysis. In: Polkowski, L., Skowron, A. (eds) Rough Sets and Current Trends in Computing. RSCTC 1998. Lecture Notes in Computer Science(), vol 1424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69115-4_11
Download citation
DOI: https://doi.org/10.1007/3-540-69115-4_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64655-6
Online ISBN: 978-3-540-69115-0
eBook Packages: Springer Book Archive