Combinatorics

Physics

Aerospace engineering

Mathematics

Poisson distribution

Algorithm

Statistics

Tolerance interval

Bernoulli's principle

Engineering

Beta-binomial distribution

Negative binomial distribution

Binomial proportion confidence interval

Continuity correction

Interval (graph theory)

Computer science

Binomial distribution

CDF-based nonparametric confidence interval

Quantum mechanics

Binomial (polynomial)

Observable

Confidence interval

Bernoulli trial

Symmetry

When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of the exact confidence interval of the sampled outcome is a mathematical challenge. This paper proposes three alternative confidence interval calculation methods that are characterized and exemplified.

Binomial Distributed Data Confidence Interval Calculation: Formulas, Algorithms and Examples