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Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
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Lothar Heinrich
Published/Copyright:
September 25, 2009
Summary
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.
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Published Online: 2009-09-25
Published in Print: 2004-01-01
© 2004 Oldenbourg Wissenschaftsverlag GmbH
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Articles in the same Issue
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- On second order minimax estimation of invariant density for ergodic diffusion
- Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
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Articles in the same Issue
- On asymptotic expansion of pseudovalues in nonparametric median regression
- On second order minimax estimation of invariant density for ergodic diffusion
- Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
- Estimation of linear functionals of bivariate distributions with parametric marginals
- A remark on the quickest detection problems
