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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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)
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)
Couso, I., Dubois, D.: Statistical reasoning with set-valued information: Ontic vs. epistemic views. Int. J. Approx. Reason. 55, 1502–1518 (2014)
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)
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)
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)
Hyndman, R.J., Fan, Y.: Sample quantiles in statistical packages. Am. Stat. 50, 361–365 (1996)
Kolacz, A., Grzegorzewski, P.: Measures of dispersion for multidimensional data. Eur. J. Oper. Res. 251, 930–937 (2016)
Martín, J., Mayor, G.: How separated Palma, Inca and Manacor are? In: Proceedings of the AGOP 2009, pp. 195–200 (2009)
Sinova, B.: M-estimators of location for interval-valued random elements. Chemometr. Intell. Lab. Syst. 156, 115–127 (2016)
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., 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)
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)
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Grzegorzewski, P. (2019). Measures of Dispersion for Interval Data. In: Destercke, S., Denoeux, T., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Uncertainty Modelling in Data Science. SMPS 2018. Advances in Intelligent Systems and Computing, vol 832. Springer, Cham. https://doi.org/10.1007/978-3-319-97547-4_13
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DOI: https://doi.org/10.1007/978-3-319-97547-4_13
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