Birnbaum-Saunders distribution: a review of models, analysis, and applications. (English) Zbl 1428.62072
Summary: In [J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)], Z. W. Birnbaum and S. C. 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.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62B10 | Statistical aspects of information-theoretic topics |
| 62F15 | Bayesian inference |
| 62N05 | Reliability and life testing |
| 62P35 | Applications of statistics to physics |
| 62-02 | Research exposition (monographs, survey articles) pertaining to statistics |
Keywords:
Bayes estimators; EM algorithm; Fisher information matrix; hazard function; length-biased distribution; moments and inverse moments; probability density function; stochastic orderings; TP\(_2\) propertyCitations:
Zbl 0209.49801References:
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