On Multivariate Log Birnbaum-Saunders Distribution

Debasis Kundu ()
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Debasis Kundu: Indian Institute of Technology Kanpur

Sankhya B: The Indian Journal of Statistics, 2017, vol. 79, issue 2, No 6, 292-315

Abstract: Abstract Univariate Birnbaum-Saunders distribution has received a considerable attention in recent years. Rieck and Nedelman (Technometrics, vol. 33, 51–60, 1991) introduced a log Birnbaum-Saunders distribution. We introduce a multivariate log Birnbaum-Saunders distribution and discuss its different properties. It is observed that the proposed multivariate model can be obtained from the multivariate Gaussian copula. We have proposed the maximum likelihood estimators of the unknown parameters. Since it is a computationally challenging problem, particularly if the dimension is high, we have considered the approximate maximum likelihood estimators based on the Copula structure using two-step procedure. The asymptotic distributions of both these estimators have been obtained. We compare their performances using Monte Carlo simulations, and it is observed that their performances are very similar in nature. One data set has been analyzed for illustrative purposes.

Keywords: Birnbaum-Saunders distribution; Gaussian copula; Fisher information matrix; Maximum likelihood estimators; Shannon entropy (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13571-016-0119-5

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