The new rank-based concentration index: Further analysis and properties

Tarald O Kvålseth

PLOS ONE, 2026, vol. 21, issue 2, 1-15

Abstract: Additional properties and generalizations are explored for a recently introduced concentration index CK. The CK is based on both the distribution of a set of proportions (probabilities) as well as their ranks. The CK is closely related to and proposed as a preferred alternative to the widely used Q that equals the sum of quadratic terms (proportions). Besides the use of CK and Q as measures of market or industry concentration, with the proportions being market shares, CK or its potential transformations can be used as alternative measures in a variety of real measurement situations for which Q has been applied. The extended analysis of CK includes the proof that CK is a convex function, which makes it capable of decomposition analysis. The sensitivity and transfer effect of CK due to changes in the distribution of the proportions is studied. Derivation is given for the so-called numbers equivalent of CK and for its probability interpretation. Generalizations of CK are considered for changing the relative emphasis of the component proportions. Randomly generated distributions exemplify the limited effect on CK from excluding the smallest proportions that are often unavailable in real situations. Numerical comparisons between CK and other concentration indices are presented for a wide variety of firms or industries. A statistical inference procedure is presented for appropriate situations.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0343034 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 43034&type=printable (application/pdf)

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:plo:pone00:0343034

DOI: 10.1371/journal.pone.0343034

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().