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The \(\beta\)-Birnbaum-Saunders distribution: an improved distribution for fatigue life modeling. (English) Zbl 1328.62572

Summary: Z. W. Birnbaum and S. C. Saunders [J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)] introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called \(\beta \)-Birnbaum-Saunders distribution is proposed for fatigue life modeling. Various properties of the new model including expansions for the moments, moment generating function, mean deviations, density function of the order statistics and their moments are derived. We discuss maximum likelihood estimation of the model’s parameters. The superiority of the new model is illustrated by means of three failure real data sets.

MSC:

62N05 Reliability and life testing
62E10 Characterization and structure theory of statistical distributions

Citations:

Zbl 0209.49801

Software:

R; Ox; Mathematica
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Full Text: DOI

References:

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