Novel closed-form point estimators for the beta distribution

• Published in: Statistical theory and related fields Vol. 9; no. 1; pp. 12 - 33
• Main Authors: Chen, Piao, Xiao, Xun
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 02.01.2025
• Subjects: Asymptotic efficiency; consistency; estimation equation; log-moment; score equation
• ISSN: 2475-4269; 2475-4277
• DOI: 10.1080/24754269.2024.2419360

In this paper, we propose and investigate novel closed-form point estimators for the beta distribution. The estimators of the first type are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments in the moment estimation equations and solve the mixed type of moment equations simultaneously. The estimators of the second type are based on an approximation to Fisher's likelihood principle. The idea is to solve two score equations derived from the log-likelihood function of generalized beta distributions. Both two resulted estimators are in closed forms, strongly consistent and asymptotically normal. In addition, through theoretical analyses and extensive simulations, the proposed estimators are shown to perform very close to the maximum likelihood estimators in both small and large samples, and they significantly outperform the method of moment estimators.