Abstract
The Kolmogorov–Smirnov goodness-of-fit test for equality of two distributions is considered. Two generalizations of this test for interval-valued data are proposed. Each version correspond to a different view on the interval outcomes of the experiment – either the epistemic or the ontic one. Each view yield its own approaches to data analysis and statistical inference.
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
References
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Heidelberg
Couso I, Dubois D (2014) Statistical reasoning with set-valued information: ontic vs epistemic views. Int J Approx Reas 55:1502–1518
Gibbons JD, Chakraborti S (2003) Nonparametric Statistical Inference, 4th edn. Marcel Dekker, New York
Grzegorzewski P (2001) Fuzzy tests - defuzzification and randomization. Fuzzy Sets Syst 118:437–446
Grzegorzewski P (2017) The Kolmogorov goodness-of-fit test for interval-valued data. In: 2017 IEEE international conference on fuzzy system, (FUZZ-IEEE), pp 1–6, https://doi.org/10.1109/FUZZ-IEEE.2017.801557
Grzegorzewski P, Szymanowski H (2014) Goodness-of-fit tests for fuzzy data. Inf Sci 288:374–386
Hesamian G, Taheri SM (2013) Fuzzy empirical distribution function: properties and application. Kybernetika 49:962–982
Kreinovich V, Servin C (2015) How to test hypotheses when exact values are replaced by intervals to protect privacy: Case of t-tests. Departamental Technical Reports (CS), Paper 892, University of Texas at El Paso
Nguyen HT, Kreinovich V, Wu B, Xiang G (2012) Computing statistics under interval and fuzzy uncertainty. Springer, Berlin
Smirnov NV (1939) Estimate of deviation between empirical distribution functions in two independent samples (in Russian). Bull Moscow Univ 2:3–16
Westfall PH (2005) Combining \(p\)-values. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics, 2nd edn. Wiley, Chichester
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Grzegorzewski, P. (2018). The Kolmogorov–Smirnov Goodness-of-Fit Test for Interval-Valued Data. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_57
Download citation
DOI: https://doi.org/10.1007/978-3-319-73848-2_57
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73847-5
Online ISBN: 978-3-319-73848-2
eBook Packages: EngineeringEngineering (R0)