### Estimation of Asymptotic Confidence Ellipses for Birnbaum-Saunders Distribution

#### Abstract

The objective of this research is to propose the maximum likelihood estimators of parameter and also construct asymptotic confidence ellipse for Birnbaum-Saunders distribution. This distribution has been used in extensive of applications, reliability analysis and biological model. The performance of the asymptotic confidence ellipses is evaluated by considering the coverage probabilities and compared with the confidence coefficient of 0.98 for sample sizes = 30, 100, 500 and 1,000; parameter =1, 3, 5, 10, 15 and 20 and parameter = 2. The program R version 3.4.3 is used for Monte Carlo simulation study with 10,000 iterations. The research results find that as the sample size is increasing, the coverage probability is also increasing and closes to the confidence coefficient of 0.98. Moreover, different values of lead to difference of coverage probability values. If the parameter equals to 15 with =500, it gives the maximum of the coverage probability with 0.9083

.

**Keywords : **Birnbaum-Saunders distribution,* *Fisher information matrix, Asymptotic confidence ellipses

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