are simulated from a right-half-normal with scale parameter $1/3$. For the distribution of the errors $\varepsilon_j$ we consider the following cases: (i) a two-piece normal distribution with parameters $\mu=0$, $\sigma=0.25$, and $\gamma=0,0.25,0.5$; and (ii) a TP SAS distribution [@R15] with parameters $\mu=0$, $\sigma=0.25$, $\gamma=0,0.25,0.5$, and $\delta=0.75$. We truncate the observations $y_j$ that are greater than $17.5$. This censoring mechanism produces samples with 15%–35% censored observations. Tables \[table:LTPNR\]–\[table:LTPSASR\] present the results of these simulations.

The overall conclusions of this extensive simulation study are that the value of the shape parameter $\gamma$ does not seem to greatly affect the performance of the MLEs, while the use of models with a tail parameter $\delta$ have a clear effect on the performance of the MLEs. The performance of the MLEs of $\delta$ in LTP $t$ and LTP SAS models for small samples is different: the bias is smaller in the LTP SAS model. However, the estimation of $\sigma$ is more accurate in the LTP $t$ model. This is, perhaps, an unsurprising conclusion, given that it is well–known that it is difficult to learn about tail parameters with small samples and that tail parameters control the tail behaviour differently in different models. However, this analysis 