Closed-form fiducial confidence intervals for some functions of independent binomial parameters with comparisons

Approximate closed-form confidence intervals (CIs) for estimating the difference, relative risk, odds ratio, and linear combination of proportions are proposed. These CIs are developed using the fiducial approach and the modified normal-based approximation to the percentiles of a linear combination of independent random variables. These confidence intervals are easy to calculate as the computation requires only the percentiles of beta distributions. The proposed confidence intervals are compared with the popular score confidence intervals with respect to coverage probabilities and expected widths. Comparison studies indicate that the proposed confidence intervals are comparable with the corresponding score confidence intervals, and better in some cases, for all the problems considered. The methods are illustrated using several examples.