in Table \[table:PBCMLE\]. We can see that the estimators obtained for the model with LTP $t$ and Log-$t$ models are close to those reported by [@D10] using a semiparametric method. The AIC values favour the models with LTP-$t$ and Log Student-$t$ (Log-$t$) errors. However, these values do not provide strong evidence to distinguish between the two models, and therefore the model choice deserves further investigation. The MLE of the skewness parameter $\gamma_{\varepsilon}$ is relatively far from zero in the Log-$t$ model. However, the inclusion of this parameter produces little effect in the estimation of the degrees of freedom $\delta_{\varepsilon}$ and the regression parameters. The 95% confidence interval for $\gamma_{\varepsilon}$ in the LTP-$t$ model is $(-0.374,0.167)$, which does not rule out the value $\gamma_{\varepsilon}=0$ as a likely value of the parameter. Then, a parsimony argument favours the model with log-Student $t$ errors (Log-$t$) in this case. Moreover, we can observe that the MLEs of $\gamma_{\varepsilon}$ in the LTP $t$ and LTP Normal model have different signs. The 95% confidence interval for $\gamma_{\varepsilon}$ in the LTP Normal model is $(-0.072,0.493)$ (which indicates that $\gamma_{\varepsilon}=0$ is an unlikely value of the parameter). The reason for this difference is that the data seem to 