Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws

Lothar Heinrich; Udo Schwingenschlögl

doi:10.1007/s00184-006-0044-0

Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws

Lothar Heinrich^*, Udo Schwingenschlögl

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Multiplier methods are used to round probabilities on finitely many categories to rational proportions. Focusing on the classical methods of Adams and Jefferson, we investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, we derive the limiting laws of the criteria, first when the rounding accuracy increases, and then when the number of categories grows large.

Original language	English (US)
Pages (from-to)	191-207
Number of pages	17
Journal	Metrika
Volume	64
Issue number	2
DOIs	https://doi.org/10.1007/s00184-006-0044-0
State	Published - Oct 2006
Externally published	Yes

Keywords

Apportionment method
Convergence in distribution
Gaussian limit law
Rounding error analysis
Sainte-Laguë divergence
q-Stationary multiplier method

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00184-006-0044-0

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abstract = "Multiplier methods are used to round probabilities on finitely many categories to rational proportions. Focusing on the classical methods of Adams and Jefferson, we investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, we derive the limiting laws of the criteria, first when the rounding accuracy increases, and then when the number of categories grows large.",

keywords = "Apportionment method, Convergence in distribution, Gaussian limit law, Rounding error analysis, Sainte-Lagu{\"e} divergence, q-Stationary multiplier method",

author = "Lothar Heinrich and Udo Schwingenschl{\"o}gl",

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AU - Schwingenschlögl, Udo

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N2 - Multiplier methods are used to round probabilities on finitely many categories to rational proportions. Focusing on the classical methods of Adams and Jefferson, we investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, we derive the limiting laws of the criteria, first when the rounding accuracy increases, and then when the number of categories grows large.

AB - Multiplier methods are used to round probabilities on finitely many categories to rational proportions. Focusing on the classical methods of Adams and Jefferson, we investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, we derive the limiting laws of the criteria, first when the rounding accuracy increases, and then when the number of categories grows large.

KW - Apportionment method

KW - Convergence in distribution

KW - Gaussian limit law

KW - Rounding error analysis

KW - Sainte-Laguë divergence

KW - q-Stationary multiplier method

UR - http://www.scopus.com/inward/record.url?scp=33749001228&partnerID=8YFLogxK

U2 - 10.1007/s00184-006-0044-0

DO - 10.1007/s00184-006-0044-0

M3 - Article

AN - SCOPUS:33749001228

SN - 0026-1335

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SP - 191

EP - 207

JO - Metrika

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IS - 2

ER -

Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws

Abstract

Keywords

ASJC Scopus subject areas

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