Zieliński (2012) showed the existence of the shortest confidence interval for a probability of success in a negative binomial distribution. The method of obtaining such an interval was presented as well. Unfortunately, the confidence interval obtained has one disadvantage: it does not keep the prescribed confidence level. In the present article, a small modification is introduced, after which the resulting shortest confidence interval does not have that disadvantage.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-4,
author = {Wojciech Zieli\'nski},
title = {The shortest randomized confidence interval for probability of success in a negative binomial model},
journal = {Applicationes Mathematicae},
volume = {41},
year = {2014},
pages = {43-49},
zbl = {1298.62054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-4}
}
Wojciech Zieliński. The shortest randomized confidence interval for probability of success in a negative binomial model. Applicationes Mathematicae, Tome 41 (2014) pp. 43-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-4/