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2019 | OriginalPaper | Chapter

Measures of Dispersion for Interval Data

Author : Przemyslaw Grzegorzewski

Published in: Uncertainty Modelling in Data Science

Publisher: Springer International Publishing

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Abstract

Almost all experiments reveal variability of their results. In this contribution we consider the measures of dispersion for sample of random intervals. In particular, we suggest a generalization of two well-known classical measures of dispersion, i.e. the range and the interquartile range, for interval-valued samples.

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Literature
1.
go back to reference Billard, L., Diday, E.: From the statistics of data to the statistics of knowledge: symbolic data analysis. J. Am. Stat. Assoc. 98, 470–487 (2003)MathSciNetCrossRef Billard, L., Diday, E.: From the statistics of data to the statistics of knowledge: symbolic data analysis. J. Am. Stat. Assoc. 98, 470–487 (2003)MathSciNetCrossRef
2.
go back to reference Blanco-Fernández, A., Corral, N., González-Rodríguez, G.: Estimation of a flexible simple linear model for interval data based on set arithmetic. Comput. Stat. Data Anal. 55, 2568–2578 (2011)MathSciNetCrossRef Blanco-Fernández, A., Corral, N., González-Rodríguez, G.: Estimation of a flexible simple linear model for interval data based on set arithmetic. Comput. Stat. Data Anal. 55, 2568–2578 (2011)MathSciNetCrossRef
3.
go back to reference Couso, I., Dubois, D.: Statistical reasoning with set-valued information: Ontic vs. epistemic views. Int. J. Approx. Reason. 55, 1502–1518 (2014)MathSciNetCrossRef Couso, I., Dubois, D.: Statistical reasoning with set-valued information: Ontic vs. epistemic views. Int. J. Approx. Reason. 55, 1502–1518 (2014)MathSciNetCrossRef
4.
go back to reference De Carvalho, F.A.T., De Souza, R.M.C.R., Chavent, M., Lechevallier, Y.: Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recogn. Lett. 27, 167–179 (2006)CrossRef De Carvalho, F.A.T., De Souza, R.M.C.R., Chavent, M., Lechevallier, Y.: Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recogn. Lett. 27, 167–179 (2006)CrossRef
5.
go back to reference de la Rosa, S., de Sáa, M.A., Lubiano, B., Sinova, P.F.: Robust scale estimators for fuzzy data. Adv. Data Anal. Classif. 11, 731–758 (2017)MathSciNetCrossRef de la Rosa, S., de Sáa, M.A., Lubiano, B., Sinova, P.F.: Robust scale estimators for fuzzy data. Adv. Data Anal. Classif. 11, 731–758 (2017)MathSciNetCrossRef
6.
go back to reference Gil, M.A., Lubiano, M.A., Montenegro, M., López, M.T.: Least squares fitting of an affine function and strenght of association for interval-valued data. Metrika 56, 97–111 (2002)MathSciNetCrossRef Gil, M.A., Lubiano, M.A., Montenegro, M., López, M.T.: Least squares fitting of an affine function and strenght of association for interval-valued data. Metrika 56, 97–111 (2002)MathSciNetCrossRef
7.
go back to reference Hyndman, R.J., Fan, Y.: Sample quantiles in statistical packages. Am. Stat. 50, 361–365 (1996) Hyndman, R.J., Fan, Y.: Sample quantiles in statistical packages. Am. Stat. 50, 361–365 (1996)
8.
go back to reference Kolacz, A., Grzegorzewski, P.: Measures of dispersion for multidimensional data. Eur. J. Oper. Res. 251, 930–937 (2016)MathSciNetCrossRef Kolacz, A., Grzegorzewski, P.: Measures of dispersion for multidimensional data. Eur. J. Oper. Res. 251, 930–937 (2016)MathSciNetCrossRef
9.
go back to reference Martín, J., Mayor, G.: How separated Palma, Inca and Manacor are? In: Proceedings of the AGOP 2009, pp. 195–200 (2009) Martín, J., Mayor, G.: How separated Palma, Inca and Manacor are? In: Proceedings of the AGOP 2009, pp. 195–200 (2009)
10.
go back to reference Sinova, B.: M-estimators of location for interval-valued random elements. Chemometr. Intell. Lab. Syst. 156, 115–127 (2016)CrossRef Sinova, B.: M-estimators of location for interval-valued random elements. Chemometr. Intell. Lab. Syst. 156, 115–127 (2016)CrossRef
11.
go back to reference Sinova, B., Casals, M.A., Colubi, A., Gil, M.A. : The median of a random interval. In: Borgelt, C., et al. (eds.) Combining Soft Computing & Statistical Methods, pp. 575–583. Springer, Heidelberg (2010) Sinova, B., Casals, M.A., Colubi, A., Gil, M.A. : The median of a random interval. In: Borgelt, C., et al. (eds.) Combining Soft Computing & Statistical Methods, pp. 575–583. Springer, Heidelberg (2010)
12.
go back to reference Sinova, B., González-Rodríguez, G., Van Aelst, S.: An alternative approach to the median of a random interval using an \(L^2\) metric. In: Kruse, R., et al. (eds.) Synergies of Soft Computing and Statistics for Intelligent Data Analysis, pp. 273–281. Springer, Heidelberg (2013)CrossRef Sinova, B., González-Rodríguez, G., Van Aelst, S.: An alternative approach to the median of a random interval using an \(L^2\) metric. In: Kruse, R., et al. (eds.) Synergies of Soft Computing and Statistics for Intelligent Data Analysis, pp. 273–281. Springer, Heidelberg (2013)CrossRef
13.
go back to reference Sinova, B., Van Aelst, S.: On the consistency of a spatial-type interval-valued median for random intervals. Stat. Probab. Lett. 100, 130–136 (2015)MathSciNetCrossRef Sinova, B., Van Aelst, S.: On the consistency of a spatial-type interval-valued median for random intervals. Stat. Probab. Lett. 100, 130–136 (2015)MathSciNetCrossRef
Metadata
Title
Measures of Dispersion for Interval Data
Author
Przemyslaw Grzegorzewski
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-97547-4_13

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