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On Small‐Sample Confidence Intervals for Parameters in Discrete Distributions
Author(s) -
Agresti Alan,
Min Yongyi
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00963.x
Subject(s) - confidence interval , mathematics , statistics , binomial proportion confidence interval , binomial (polynomial) , coverage probability , tolerance interval , confidence distribution , nominal level , cdf based nonparametric confidence interval , sample size determination , binomial distribution , robust confidence intervals , interval estimation , negative binomial distribution , poisson distribution
Summary. The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two‐sided test than inverting two separate one‐sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.