Article
Title: On Multivariate Log Birnbaum-Saunders Distribution
Author(s): Debasis Kundu
Issue: Volume 79 Series B Part 2 Year 2017
Pages: 292 -- 315
Abstract
Univariate Birnbaum-Saunders distribution has received a considerable at-
tention 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.