Asymptotic confidence ellipses of parameters for the Birnbaum-Saunders distribution

The purpose of this study is to find the suitable covariance matrix for the construction of confidence regions of parameters in the Birnbaum-Saunders distribution and we need to calculate confidence ellipses and compare the coverage probabilities for asymptotic confidence ellipses of parameters in the Birnbaum-Saunders distribution. Monte Carlo simulation is used to compare the coverage probabilities of the asymptotic confidence ellipses. The result showed that the asymptotic confidence ellipses can work very well when the alpha values increase more than 2.0 and the sample sizes (n) increase. In the Birnbaum-Saunders distribution, we can use method of moment estimators instead of maximum likelihood estimators for confidence ellipses because of high efficiency of coverage probabilities.