Algorithm 2. Generating a adaptive Type-II progressive hybrid censored sample from the GB distribution.

Step1: Generate $m$ independent observations $Z_1,Z_2,\dots ,Z_m$, where $Z_i$ follows the uniform distribution $U(0,1)$, $i=1,2,\dots ,m$.

Step 2: For the known censoring scheme $(R_1,R_2,\dots ,R_m)$, let ${\xi }_i=Z_i{}^{1/(i+R_m+R_{m-1}+\dots +R_{m-i+1})},i=1,2,\dots ,m$.

Step 3: By setting $U_i=1-{\xi }_m{\xi }_{m-1}\dots {\xi }_{m-i+1}$, then $U_1,U_2,\dots ,U_m$ is a Type-II progressive censored sample from the uniform distribution $U(0,1)$.

Step 4: Using the inverse transformation $X_{i:m:n}=F^{-1}(U_i)$, $i=1,2,\dots ,m$, we obtain a Type-II progressive censored sample from the GB distribution; that is, $X_{1:m:n},X_{2:m:n},\dots ,X_{m:m:n}$, where $F^{-1}(\cdot )$ denotes the GB distribution’s inverse cumulative functional expression with the parameter $(\beta ,\lambda )$. The following theorem1 gives the uniqueness of the solution for the equation $X_{i:m:n}=F^{-1}(U_i)$, $i=1,2,\dots ,m$.

Step 5: If there exists a real number $J$ satisfying $X_{\mathrm{J}:\mathrm{m}:\mathrm{n}}<T\le X_{\mathrm{J}+1:\mathrm{m}:\mathrm{n}}$, then we set index $J$ and record $X_{1:m:n},X_{2:m:n},\dots ,X_{J+1:m:n}$.

Step 6: Generate the first $m-J-1$ order statistics $X_{J+2:m:n},X_{J+3:m:n},\dots ,X_{m:m:n}$ from the truncated distribution $f(x;\beta ,\lambda )/[1-F(x_{J+1};\beta ,\lambda )]$ with a sample size $n-J-1-{\displaystyle {\sum }_{i=1}^J{R}_i}$.