A simplified Wilson-type confidence interval for binomial proportions

Name: Chalermsak Mayoo

Organization : King Mongkut's University of Technology North Bangkok. Department of Applied Statistics, Faculty of Science

Email : sab_chula@hotmail.com

LCSH: Confidence intervals

LCSH: Binomial distribution

LCSH: Estimation theory

LCSH: Asymptotic distribution (Probability theory)

LCSH: Numerical analysis

LCSH: Probabilities -- Mathematical models

Abstract: Confidence interval estimation for a binomial proportion remains a fundamental problem in statistical inference, particularly for small and moderate sample sizes where the classical Wald interval is known to exhibit substantial undercoverage. In this study, we investigate a simplified Wilson-type confidence interval obtained by approximating the Wilson score interval and incorporating a pseudo-count adjustment in the estimator of the binomial proportion. The resulting interval has a closed-form expression that is computationally simple while preserving the stability properties of the Wilson approach. In particular, it can be shown that the proposed interval is asymptotically equivalent to the Wilson score interval, providing theoretical justification for the pseudo-count adjustment used in practice. The finite-sample performance of the proposed interval is evaluated through a comprehensive numerical study and compared with several widely used methods, including the Wald, Wilson, Agresti–Coull, Brown–Cai–DasGupta, and arcsine intervals. Performance is assessed in terms of average coverage probability, average expected length, and root mean square error across multiple sample sizes and nominal confidence levels. The results indicate that the simplified Wilson-type interval maintains coverage probabilities close to the nominal level and achieves competitive interval lengths across a wide range of scenarios. These findings suggest that the proposed formulation provides a practical and computationally convenient alternative for confidence interval estimation of binomial proportions.

King Mongkut's University of Technology North Bangkok. Central Library

Address: BANGKOK

Email: library@kmutnb.ac.th

Created: 2026

Modified: 2026-06-30

Issued: 2026-06-30

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BibliograpyCitation : ใน มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ. คณะวิทยาศาสตร์ประยุกต์. การประชุมวิชาการระดับชาติด้านสถิติ วิทยาศาสตร์ข้อมูล และการประกันภัย ครั้งที่ 3 (NCSDI 2026) (pp.29-34). กรุงเทพฯ : มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ

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