Mapping Research on the Birnbaum–Saunders Statistical Distribution: Patterns, Trends, and Scientometric Perspective
Year: 2025
Type: article
Study design: Systematic Review
Abstract: This article provides a critical assessment of the Birnbaum–Saunders (BS) distribution, a pivotal statistical model for lifetime data analysis and reliability estimation, particularly in fatigue contexts. The model has seen successfully applied across diverse fields, including biological mortality, environmental sciences, medicine, and risk models. Moving beyond a basic scientometric review, this study synthesizes findings from 353 peer-reviewed articles, selected using PRISMA 2020 protocols, to specifically trace the evolution of estimation techniques, regression methods, and model extensions. Key findings reveal robust theoretical advances, such as Bayesian methods and bivariate/spatial adaptations, alongside practical progress in influence diagnostics and software development. The analysis highlights key research gaps, including the critical need for scalable, auditable software and structured reviews, and notes a peak in scholarly activity around 2019, driven importantly by the Brazil-Chile research alliance. This work offers a consolidated view of current BS model implementations and outlines clear future directions for enhancing their theoretical robustness and practical utility.
Source: Stats
DOI: 10.3390/stats8040116
Author: Víctor Leiva
Institution: Pontificia Universidad Católica de Valparaíso
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W4417316741