Optimal sample size for the Birnbaum-Saunders distribution under a decision-theoretic approach

TL;DR

This paper introduces a decision-theoretic methodology to determine the optimal sample size for estimating the mean of the Birnbaum-Saunders distribution, including practical R tools.

Contribution

It proposes the first methodology for optimal sample size determination for the Birnbaum-Saunders distribution's mean estimation, incorporating loss functions and computational tools.

Findings

Developed a decision-theoretic framework for sample size calculation.

Created R tools for practical implementation.

Addressed a gap in sample size determination for this distribution.

Abstract

The Birnbaum-Saunders distribution has been widely applied in several areas of science and although several methodologies related to this distribution have been proposed, the problem of determining the optimal sample size for estimating its mean has not yet been studied. For this purpose, we propose a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider loss functions for point and interval inference. Finally, computational tools in the R language were developed to use in practice.