September 24, 2025Open Access

A unified method for generating closed-form point estimators for exponential families: An example with the beta distribution applied to proportions of land used for farming

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Monte Carlo simulation evaluates closed-form estimators for beta distribution parameters, suggesting practical applications.

Closed-form point estimators are derived for exponential families, enhancing modeling of multi-parameter cases.
The approach recovers several previous estimators and introduces new families indexed by monotone transformations.
Monte Carlo simulation assesses the performance of both proposed and existing estimators, providing comparative insights.
The methodology is applied to a novel dataset on land proportions used for farming in Roraima, Brazil, showcasing practical use.

Vila et al. (2025) studied this question.

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