Exact Confidence Intervals in Distributions with One Parameter
Year: 2026
Type: article
Abstract: The Clopper–Pearson method of constructing a confidence interval for the probability of success in a binary population that follows a Bernoulli distribution is well known. This paper pedagogically justifies the Clopper–Pearson method and extends the method to all distributions with one parameter whose cumulative probability distribution functions are monotonically continuous with respect to their single parameter. The conservativeness of Clopper–Pearson confidence intervals is proved analytically. Clopper–Pearson confidence intervals are constructed for Poisson, geometric, non-central hyper-geometric, and exponential, etc. It turns out that such extensions result in various well-known confidence intervals in the literature.
Source: Foundations
Author: Xianggui Qu
Institution: Oakland University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W7168465371