previously. In our first simulation scenario, we simulate $N=10,000$ samples of sizes $n=30,50,100,250,500,1000$ from a LTP normal (log two-piece normal) with different combinations of the parameter values: $\mu=0$, $\sigma=1$, and $\gamma=0,0.25,0.5,0.75$. Negative values of $\gamma$ would induce similar results, since they produce the corresponding reflected density about $e^{\mu}$, and are therefore omitted. For each of these samples, we calculate the corresponding MLEs, using the R command ‘optim’, and calculate the bias, variance, and root-mean-square error (RMSE) of these. In our second simulation scenario, we simulate $N=10,000$ samples from a LTP $t$ (log two-piece Student-$t$) with parameters: $\mu=0$, $\sigma=1$, $\gamma=0,0.25,0.5,0.75$, and $\delta=1$. The third simulation scenario is analogous to the second scenario, with $\delta=2$. In the fourth scenario, we simulate $N=10,000$ samples from a LTP SAS with parameters : $\mu=0$, $\sigma=1$, $\gamma=0,0.25,0.5,0.75$, and $\delta=0.75$. Tables \[table:LTPN\]–\[table:LTPSAS2\] present the results of these simulations.

In second class of simulations, we investigate the performance of the use of log two-piece errors in AFT models (\[AFTModel\]). For this purpose, we simulate from the linear regression model: $$\begin{aligned}
\log(y_j) = {\bf x}_j^{\top}\bm{\beta} + \varepsilon_j, \,\,\, j=1,\dots,n,\end{aligned}$$ with $n=100,250,500$, $\beta = (1,2,3)^{\top}$, and ${\bf x}_j = (1,x_{j1},x_{j2})^{\top}$. The second and third entries of the covariates ${\bf x}_j$ 