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Lothar Heinrich, Friedrich Pukelsheim, Udo Schwingenschlögl
Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
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.
Statistics & Decisions, Oldenbourg Wissenschaftsverlag
Print ISSN: 0721-2631
Volume: 22, 01/2004
Pages: 043 - 059