Abstract
Some properties of a previously defined index of diversity (Beran, 1994) are derived. Based on a bivariate generalization of this index, a measure of association, the codiversity, is developed, and a geometrical representation is given. If two variables A and B are viewed as input and output variables, respectively, an algorithm for optimizing the codiversity of the system is outlined and applied to an example demonstrating its usefulness in the design of experiments.
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
Preview
Unable to display preview. Download preview PDF.
References
Adam, A. (1963): Systematische Datenverarbeitung bei der Auswertung von Versuchs-und Beobachtungsergebnissen. Physica, Würzburg.
Adam, A. (1984): Grundriß einer statistischen Systemtheorie. In: Festschrift für Wilhelm Winkler (Hrsg.: A. Adam). Schriftenreihe der Österreichischen Statistischen Gesellschaft, Bd. 1., Orac, Wien.
Beran, H. (1994): Eine systemkonforme Maßzahlbildung für klassifikatorische Merkmale. OR Spektrum 16, 81–88.
Fano, R.M. (1966): Informationsübertragung. R. Oldenbourg, München - Wien.
Ferschl, F. (1985). Deskriptive Statistik, 3. A., Physica, Würzburg -Wien.
Hill, M.O. (1973): Diversity and Evenness: A Unifying Notation and its Consequences. Ecology 54, 427–432.
Hurlbut, S.H. (1971): The Nonconcept of Species Diversity: A Critique and Alternative Parameters. Ecology 52, 577–586.
Kämmerer, W. (1974): Einführung in mathematische Methoden der Kybernetik. Akademie-Verlag, Berlin.
Patil, G.P.; Taillie, C. (1982): Diversity as a Concept and its Measurement. J. Am. Stat. Assoc., 77: 548–567.
Peters, J. (1967): Einführung in die allgemeine Informationstheorie. Kommunikation und Kybernetik in Einzeldarstellungen, Bd. 6, Springer, Berlin - Heidelberg - New York.
Rao, C.R. (1982): Analysis of Diversity: A Unified Approach. In: Statistical Decision Theory and Related Topics III, Vol. 2. Academic Press, London–New York–Toronto, 233–250.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Beran, H. (1999). A Generalization and Optimization of a Measure of Diversity. In: Leopold-Wildburger, U., Feichtinger, G., Kistner, KP. (eds) Modelling and Decisions in Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12519-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-12519-9_8
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2462-9
Online ISBN: 978-3-662-12519-9
eBook Packages: Springer Book Archive