Novel Closed-form Point Estimators for the Beta Distribution

TL;DR

This paper introduces new closed-form estimators for the beta distribution that are simple, consistent, and perform comparably to maximum likelihood estimators, improving upon traditional moment-based methods.

Contribution

It proposes two novel closed-form estimators for the beta distribution, based on modified moments and likelihood approximations, with proven consistency and asymptotic normality.

Findings

Estimators are strongly consistent and asymptotically normal.

Proposed estimators perform close to ML estimators in simulations.

They outperform traditional moment estimators in accuracy.

Abstract

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.