Some Numerical Comparisons of Several Approximations to the Binomial Distribution
作者:
Friedrich Gebhardt,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1969)
卷期:
Volume 64,
issue 328
页码: 1638-1646
ISSN:0162-1459
年代: 1969
DOI:10.1080/01621459.1969.10501083
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Several approximations to the binomial distribution were compared in 1956 by Raff [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(1/n). In 1963, Bol'shev [2] gave two new Poisson-Type approximations. In this paper, some of Raff's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values ofpwhile the Camp-Paulson and Borges' approximations should generally be preferred for largep.
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