2022/10/11 by Piao Chen, Xun Xiao, Chen, Piao +1 · 1 citation
Decision Sciences · Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2210.05536
openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators 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 second estimators 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 extensive simulations, the proposed estimators are shown to perform very close to the ML estimators in both small and large samples, and they significantly outperform the moment estimators.