Algorithm 2.

Step 1: Generate sample from the Birnbaum-Saunders distribution

Step 2: At the $b$ step

(a) Generate $x^{\ast }=(x_1^{\ast },x_2^{\ast },...,x_n^{\ast })$ with replacement from $x=(x_1,x_2,...,x_n)$

(b) Compute $\hat{b}(\hat{\alpha },\alpha )$ using Eq. (7) and compute $\hat{b}(\hat{\beta },\beta )$ using Eq. (8)

(c) Compute $\widetilde{{\alpha }_k}$ using Eq. (9) and $\widetilde{{\beta }_k}$ using Eq. (10)

(d) Compute ${\hat{\theta }}_k$ using Eq. (11)

Step 3: Repeat step 2, a total B times and obtain an array of ${\hat{\theta }}_k$’s

Step 4: Compute $L_{\theta .B}={\hat{\theta }}_k(\gamma /2)$ and $U_{\theta .B}={\hat{\theta }}_k(1-\gamma /2)$