Algorithm 1 The MCMC method

Step 1: Choose the initial value $({\beta }^{(0)},{\lambda }^{(0)})$.

Step 2: At stage $i$ and for the given m, n and ATII-PH censored data, generate ${\beta }^{(i)}$ from the following:

$Gamma(m+a, b+2{\displaystyle {\sum }_{i=1}^m{x}_i^{\lambda }+}2{\displaystyle {\sum }_{i=1}^D{R}_i{x}_i^{\lambda }+}2R^{*}{x}_m^{\lambda }).$

Step 3: Generate ${\lambda }^{(i)}$ from ${\pi }_2({\lambda }^{(i-1)}|{\beta }^{(i)},\overrightarrow{x})$ using the following steps.

Step 3-1: Generate ${\lambda }^{\prime }$ from $N({\lambda }^{(i-1)},\mathrm{var}(\lambda ))$.

Step 3-2: Generate the $\omega$ from the uniform distribution U(0, 1).

Step 3-3: Set ${\lambda }^{(i)}=\{\begin{array}{c}{\lambda }^{\prime },\hspace{1em}\begin{array}{cc}& if\omega \le r^{\ast }\end{array}\\ {\lambda }^{(i-1)},\begin{array}{ccc}& if\omega >r^{\ast }& \end{array}\end{array}$, where $r^{\ast }=\min \{1,\frac{{\pi }_2({\lambda }^{\prime }|{\beta }^{(i)},\overrightarrow{x})}{{\pi }_2({\lambda }^{(i-1)}|{\beta }^{(i)},\overrightarrow{x})}\}$.

Step 4: Set $i=i+1$.

Step 5: By repeating Steps 2–4 N times, we get $({\beta }_1,{\lambda }_1),({\beta }_2,{\lambda }_2),\dots ,({\beta }_N,{\lambda }_N)$. Furthermore, we compute $H_1,H_2,\dots ,H_N$, where $H_i=H({\beta }_i,{\lambda }_i), i=1,2,\dots ,N$ and $H(\beta ,\lambda )$ is the Shannon entropy of the GB distribution.