favour a model with lighter tails than those of the lognormal distribution. The 95% confidence intervals for the parameters $\gamma$ and $\delta$ (obtained as the 0.147-level profile likelihood intervals, see [@K85]) in the LTP SAS model are $(0.31,0.53)$ and $(1.02, 1.56)$, respectively. It is worth noticing that the confidence interval for $\delta$ only include values greater than one, which are associated to tails lighter than normal. Figures \[fig:NFM\]a–\[fig:NFM\]c show the probability plots and hazard functions corresponding to the LTP SAS, lognormal, and Weibull models, which visually illustrates the fit of these models. From Figure \[fig:NFM\]d We can observe that the fitted Gamma model produces an increasing hazard function, while the LTP SAS model produces a non monotonic hazard function with decreasing tail. This behaviour coincides with that of the fitted kernel estimation of the hazard function (which was obtained using lognormal kernels).

     Model      $\hat\mu$   $\hat\sigma$    $\hat\gamma$   $\hat\delta$         AIC
  ------------ ----------- --------------- -------------- -------------- -----------------
    LTP $t$       2.59          1.04            0.40          111.90          5401.80
    LTP SAS       2.63          1.39            0.42           1.22       [**5395.71**]{}
   LTP Normal     2.59          1.05            0.40            –             5398.45
   Log-normal     1.91          1.08             –              –             5443.70
    Weibull         –       (scale) 11.27   (shape) 1.08        –             5415.40
     Gamma          –       (scale) 9.31    (shape) 1.17        –             5411.11

  : Nerve data: 