Premium
Better approximate confidence intervals for a binomial parameter
Author(s) -
BÖHNING Dankmar
Publication year - 1994
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315584
Subject(s) - binomial proportion confidence interval , mathematics , confidence interval , poisson distribution , bernoulli trial , cdf based nonparametric confidence interval , confidence distribution , poisson binomial distribution , statistics , binomial distribution , bayes' theorem , binomial (polynomial) , credible interval , binomial approximation , robust confidence intervals , bernoulli's principle , negative binomial distribution , beta binomial distribution , bayesian probability , engineering , aerospace engineering
This paper discusses five methods for constructing approximate confidence intervals for the binomial parameter Θ, based on Y successes in n Bernoulli trials. In a recent paper, Chen (1990) discusses various approximate methods and suggests a new method based on a Bayes argument, which we call method I here. Methods II and III are based on the normal approximation without and with continuity correction. Method IV uses the Poisson approximation of the binomial distribution and then exploits the fact that the exact confidence limits for the parameter of the Poisson distribution can be found through the x 2 distribution. The confidence limits of method IV are then provided by the Wilson‐Hilferty approximation of the x 2 . Similarly, the exact confidence limits for the binomial parameter can be expressed through the F distribution. Method V approximates these limits through a suitable version of the Wilson‐Hilferty approximation. We undertake a comparison of the five methods in respect to coverage probability and expected length. The results indicate that method V has an advantage over Chen's Bayes method as well as over the other three methods.