Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law

Heinrich Lothar, Pukelsheim Friedrich and Schwingenschlögl Udo

Statistics & Risk Modeling, 2004, vol. 22, issue 1, 43-60

Abstract: For rounding arbitrary probabilities on finitely many categories to rational proportions, the multiplier method with standard rounding stands out. Sainte-Laguë showed in 1910 that the method minimizes a goodness-of-fit criterion that nowadays classifies as a chi-square divergence. Assuming the given probabilities to be uniformly distributed, we derive the limiting law of the Sainte-Laguë divergence, first when the rounding accuracy increases, and then when the number of categories grows large. The latter limit turns out to be a Lévy-stable distribution.

Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1524/stnd.22.1.43.32717 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

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:bpj:strimo:v:22:y:2004:i:1/2004:p:43-60:n:4

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/stnd.22.1.43.32717

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().