Multivariate Birnbaum-Saunders distribution: properties and associated inference

• Published in: Journal of statistical computation and simulation Vol. 85; no. 2; pp. 374 - 392
• Main Authors: Lemonte, Artur J., Martínez-Florez, Guillermo, Moreno-Arenas, Germán
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 22.01.2015; Taylor & Francis Ltd
• Subjects: Birnbaum-Saunders distribution; Computation; Computer simulation; conditional specifications; Crack propagation; Fatigue failure; Fatigue life; fatigue life distribution; lifetime data; Mathematical models; Modelling; Multivariate analysis; multivariate distributions; Normal distribution; Parameter estimation; Reliability
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2013.823964

The univariate fatigue life distribution proposed by Birnbaum and Saunders [A new family of life distributions. J Appl Probab. 1969;6:319-327] has been used quite effectively to model times to failure for materials subject to fatigue and for modelling lifetime data and reliability problems. In this article, we introduce a Birnbaum-Saunders (BS) distribution in the multivariate setting. The new multivariate model arises in the context of conditionally specified distributions. The proposed multivariate model is an absolutely continuous distribution whose marginals are univariate BS distributions. General properties of the multivariate BS distribution are derived and the estimation of the unknown parameters by maximum likelihood is discussed. Further, the Fisher's information matrix is determined. Applications to real data of the proposed multivariate distribution are provided for illustrative purposes.