Basic statistics for distributional symbolic variables: a new metric-based approach

Antonio Irpino () and Rosanna Verde ()

Advances in Data Analysis and Classification, 2015, vol. 9, issue 2, 143-175

Abstract: In data mining it is usual to describe a group of measurements using summary statistics or through empirical distribution functions. Symbolic data analysis (SDA) aims at the treatment of such kinds of data, allowing the description and the analysis of conceptual data or of macrodata summarizing classical data. In the conceptual framework of SDA, the paper aims at presenting new basic statistics for distribution-valued variables, i.e., variables whose realizations are distributions. The proposed measures extend some classical univariate (mean, variance, standard deviation) and bivariate (covariance and correlation) basic statistics to distribution-valued variables, taking into account the nature and the variability of such data. The novel statistics are based on a distance between distributions: the $$\ell _2$$ ℓ 2 Wasserstein distance. A comparison with other univariate and bivariate statistics presented in the literature points out some relevant properties of the proposed ones. An application on a clinic dataset shows the main differences in terms of interpretation of results. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Wasserstein metric; Symbolic data; Distribution-valued data; Histogram data; Basic statistics; 62-07; 62A99 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11634-014-0176-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:advdac:v:9:y:2015:i:2:p:143-175

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-014-0176-4

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from Springer, German Classification Society - Gesellschaft für Klassifikation (GfKl), Japanese Classification Society (JCS), Classification and Data Analysis Group of the Italian Statistical Society (CLADAG), International Federation of Classification Societies (IFCS)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().