Abstract
The two-sample dispersion testing problem is considered. Two generalizations of the Sukhatme test for interval-valued data are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment: the epistemic or the ontic one. Each view yields its own approach to data analysis which results in a different test construction and the way of carrying on the statistical inference.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aumann, R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)
Blanco-Fernández, A., Casals, M.R., Colubi, A., Corral, N., García-Bárzana, M., Gil, M.A., González-Rodríguez, G., López, M.T., Lubiano, M.A., Montenegro, M., Ramos-Guajardo, A.B., de la Rosa de Sáa, S., Sinova S.: A distance-based statistic analysis of fuzzy number-valued data. Int. J. Approx. Reason. 55, 1487–1501, 1601–1605 (2014)
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)
Gibbons, J.D., Chakraborti, S.: Nonparametric Statistical Inference. Marcel Dekker, New York (2003)
Grzegorzewski, P.: Fuzzy tests - defuzzification and randomization. Fuzzy Sets Syst. 118, 437–446 (2001)
Nguyen, H.T., Kreinovich, V., Wu, B., Xiang, G.: Computing Statistics under Interval and Fuzzy Uncertainty. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-24905-1
Ramos-Guajardo, A.B., Colubi, A., González-Rodríguez, G., Gil, M.A.: One-sample tests for a generalized Fréchet variance of a fuzzy random variable. Metrika 71, 185–202 (2010)
Ramos-Guajardo, A.B., Colubi, A., González-Rodríguez, G.: Inclusion degree tests for the Aumann expectation of a random interval. Inf. Sci. 288, 412–422 (2014)
Ramos-Guajardo, A.B., Lubiano, M.A.: K-sample tests for equality of variances of random fuzzy sets. Comput. Stat. Data Anal. 56, 956–966 (2012)
Sinova, B., Colubi, A., Gil, M.A., González-Rodríguez, G.: Interval arithmetic-based linear regression between interval data: discussion and sensitivity analysis on the choice of the metric. Inf. Sci. 199, 109–124 (2012)
Sukhatme, B.V.: On certain two sample nonparametric tests for variances. Ann. Math. Stat. 28, 188–194 (1957)
Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread. Inf. Sci. 179, 3964–3972 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Grzegorzewski, P. (2018). Two-Sample Dispersion Tests for Interval-Valued Data. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-91479-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91478-7
Online ISBN: 978-3-319-91479-4
eBook Packages: Computer ScienceComputer Science (R0)