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Birnbaum‐Saunders distribution: A review of models, analysis, and applications

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  • N. Balakrishnan
  • Debasis Kundu

Abstract

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.

Suggested Citation

  • N. Balakrishnan & Debasis Kundu, 2019. "Birnbaum‐Saunders distribution: A review of models, analysis, and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(1), pages 4-49, January.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:1:p:4-49
    DOI: 10.1002/asmb.2348
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    References listed on IDEAS

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    1. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
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    1. Kalanka P. Jayalath, 2024. "Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    2. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Saulo, Helton & Balakrishnan, Narayanaswamy & Vila, Roberto, 2023. "On a quantile autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 425-448.
    4. Kalanka P. Jayalath, 2021. "Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler," Stats, MDPI, vol. 4(2), pages 1-15, May.
    5. Zhu, Xiaojun & Liu, Kai & He, Mu & Balakrishnan, N., 2021. "Reliability estimation for one-shot devices under cyclic accelerated life-testing," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    6. Yann Dijoux, 2020. "Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 891-916, September.
    7. Aline B. Tsuyuguchi & Gilberto A. Paula & Michelli Barros, 2020. "Analysis of correlated Birnbaum–Saunders data based on estimating equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 661-681, September.
    8. Ruijie Guan & Xu Zhao & Weihu Cheng & Yaohua Rong, 2021. "A New Generalized t Distribution Based on a Distribution Construction Method," Mathematics, MDPI, vol. 9(19), pages 1-36, September.
    9. Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    10. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    11. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    12. Chanseok Park & Min Wang, 2024. "Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm," Mathematics, MDPI, vol. 12(11), pages 1-17, June.

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