2018
DOI: 10.3390/risks6010021
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Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Abstract: Abstract:Since its origins and numerous applications in material science, the Birnbaum-Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum-Saunders and log-Birnbaum-Saunders distributions in univariate and multivariate versions.… Show more

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Cited by 20 publications
(12 citation statements)
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References 94 publications
(101 reference statements)
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“…Estimation methods for the regression parameters upon a high censoring may be studied by a mixture structure [53][54][55]. (iii) An extension of the present study to the multivariate case is also of practical relevance [52,56,57].…”
Section: Conclusion Discussion and Future Researchmentioning
confidence: 99%
“…Estimation methods for the regression parameters upon a high censoring may be studied by a mixture structure [53][54][55]. (iii) An extension of the present study to the multivariate case is also of practical relevance [52,56,57].…”
Section: Conclusion Discussion and Future Researchmentioning
confidence: 99%
“…For the multivariate and matrix‐variate cases, there are open problems, including those on generalized and related distributions (eg, BS‐ t and BS‐elliptical), and estimation methods in both classical and Bayesian approaches, which can be built upon the works of, for example, Cancho et al, Caro‐Lopera et al, Paula et al, Kundu et al, and Aykroyd et al…”
Section: Distributionsmentioning
confidence: 99%
“…An additional note would be on the potential applications of the BS regression, BS‐ACD, and related models. Issues on heteroskedasticity, nonlinearity, time series characteristics, prior information and restrictions, and/or the Bayesian approach involved in model formulation, estimation, inference, and diagnostics are paid extensive attention in, for example, econometrics, finance, and insurance in terms of both research and practice (see, eg, the works of Ahmed et al, Paula et al, Liu et al, Santos‐Neto et al, and Aykroyd et al). It would be useful to obtain further developed methodologies and applications of the BS‐based and related models addressing these mentioned issues.…”
Section: Regression Estimation and Diagnosticsmentioning
confidence: 99%
“…The recent article by Aykroyd et al also includes a review of multivariate Birnbaum‐Saunders distributions and applications. Work on multivariate Birnbaum‐Saunders models and their applications was presented by Marchant et al, and applications of multivariate Birnbaum‐Saunders distributions in spatial modeling appeared in the works of Garcia‐Papani et al In addition, multivariate cumulative damage models and their relationship with time of occurrence in the context of multicomponent systems were recently derived by Fierro et al…”
Section: Introductionmentioning
confidence: 99%