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On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence

Heinrich Lothar, Pukelsheim Friedrich and Schwingenschlögl Udo

Statistics & Risk Modeling, 2005, vol. 23, issue 2/2005, 117-129

Abstract: Stationary multiplier methods are procedures for rounding real probabilities into rational proportions, while the Sainte-Laguë divergence is a reasonable measure for the cumulative error resulting from this rounding step. Assuming the given probabilities to be uniformly distributed, we show that the Sainte-Laguë divergences converge to the Lévy-stable distribution that obtains for the multiplier method with standard rounding. The norming constants to achieve convergence depend in a subtle way on the stationary method used.

Date: 2005
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