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The generalized Birnbaum-Saunders distribution and its theory, methodology, and application. (English) Zbl 1136.62016

Summary: We discuss the class of generalized Z. W. Birnbaum and S. C. Saunders distributions [J. Appl. Probab. 6, 328–347 (1969; Zbl 0216.22702)], which is a very flexible family suitable for modeling lifetime data as it allows for different degrees of kurtosis and asymmetry and unimodality as well as bimodality. We describe the theoretical developments of this model including properties, transformations and related distributions, life time analysis, and shape analysis. We also discuss methods of inference based on uncensored and censored data, diagnostics methods, goodness-of-fit tests, and random number generation algorithms for the generalized Birnbaum-Saunders model. Finally, we present some illustrative examples and show that this distribution fits the data better than the classical Birnbaum-Saunders model.

MSC:

62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory

Citations:

Zbl 0216.22702

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References:

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