0.0019             0.0016            0.0277
           30         0.5747           0.2965         0.3216      3$\times10^4$    0.5529          0.2977             0.3092         2$\times10^4$
           50         0.3827           0.2237         0.2165      1$\times10^4$    0.3714          0.2226             0.2103            6553.9
          100         0.2428           0.1470         0.1382          277.2        0.2360          0.1465             0.1345            2271.3
          250         0.1426           0.0902         0.0835         0.3965        0.1399          0.0906             0.0809            0.3979
          500         0.1011           0.0629         0.0583         0.2491        0.0981          0.0629             0.0566            0.2490
          1000        0.0711           0.0445         0.0410         0.1694        0.0690          0.0443             0.0398            0.1677

  : Simulation results: LTP $t$, $\delta=2$.[]{data-label="table:LTPt21"}

Applications {#NumericalExamples}
============

In this section, we present several medical applications with real data that illustrate the performance and usefulness of the proposed distributions. Throughout, we adopt the epsilon-skew parameterisation $\{a(\gamma),b(\gamma)\}=\{1-\gamma,1+\gamma\}$, $\gamma \in (-1,1)$, for the LTP distributions.

Example 1: Nerve data
---------------------

In our first example we analyse the data set reported in [@CL66] which contains $n=799$ observations rounded to the nearest half in units of 1/50 second, which correspond to the time between $800$ successive pulses along a nerve fibre. We consider two baseline distributions $s$ in (\[LTPPDF\]): a Student $t$ density with $\delta>0$ degrees of freedom (LTP $t$), and a symmetric sinh-arcsinh density [@JP09; @R15] (LTP SAS). The choice for these two baseline densities is motivated as follows. The Student-$t$ distribution is a parametric family of distributions with heavier tails than the normal ones; 