Distribution inequalities for the binomial law
type: Item
instance of: scholarly article
title: Distribution inequalities for the binomial law
zbMATH Open document ID: 0358.60015
author: Eric V. Slud
published in: The Annals of Probability
publication date: 1977-01-01T00:00:00Z
review text: The main theorem is the following inequality between binomial and their approximating normal tail probabilities: if \(p\leq1/4\) and \(k\geq np\), or if \(p\leq1/2\) and \(np\leq k\leq n(1-p)\), then the binomial probability \(\sum\limits_{j=k}^nb(j,n,p)\geq1-\Phi((k-np)/(npq)^{1/2})\). The tools of proof are elementary. The point of view taken is that such distribution inequalities reveal systematic errors in the common approximations used in tests of significance. The results are applied directly to construct significance tests concervative with respect to type II errors.
reviewed by: Eric V. Slud
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 3558649
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176995801
OpenAlex ID: W2005306124
DOI: 10.1214/AOP/1176995801
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description: scientific article; zbMATH DE number 3558649