A comprehensive estimator for the Fréchet distribution: asymptotical efficiency, and practical applications to health studies.

Abstract

The Fréchet distribution is a fundamental tool in extreme value theory, with applications spanning various fields such as life testing, modeling extreme health-related events (such as infant birth weight extremes or rare disease outbreaks), natural disasters, and environmental sciences. Despite its widespread use, existing parameter estimation methods for the Fréchet distribution face significant limitations, including computational inefficiency, instability with large datasets, and restrictions on the parameter space. To address these challenges, we propose an asymptotically efficient, closed-form estimator for the Fréchet distribution. Our estimator overcomes the limitations of existing methods, providing computational speed, stability, and high estimation quality across both small and large samples. Simulation studies demonstrate the superior performance of the proposed method compared to alternative approaches. Its practical utility is illustrated through its application to the National Center for Health Statistics birth dataset. To further support its adoption, an R package has been developed to enable seamless integration of the method into diverse research applications.