An improved score interval with a modified midpoint for a binomial proportion

Abstract

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method.

Keywords:

• binomial distribution
• confidence interval
• coverage probability
• score interval
• downward spikes

Acknowledgements

The research was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (No. 12XNI004).