the parameters of LTP distributions are the same as the MLEs of the parameters of the underlying two-piece distribution for the sample $\log({\bf T}) = [\log(T_1),\dots,$ $\log(T_n)]$. Inferential aspects of 3- and 4-parameter two-piece distributions have been largely discussed. For example, [@A05] show that, under certain regularity conditions on the baseline density $s$ in (\[TP2\]), the maximum likelihood estimators of the parameters of these distributions are consistent and asymptotically normal under the epsilon-skew parameterisation. [@JA10] and [@RS14] study some parameterisations that induce parameter orthogonality between the parameters $\mu$ and $\sigma$, showing that the epsilon-skew parameterisation induces this property. Parameter orthogonality, in turn implies a good asymptotic behaviour of the MLE [@JA10]. In most cases, the MLE is not available in closed-form, and it has to be obtained numerically.

Samples containing censored observations are common in the context of survival analysis. The most common types of censoring in this context correspond to:

(i) Left-censoring: when the phenomenon of interest has already occurred before the start of the study. A left-censored observation is an interval of the type $[0,T_j)$, where $T_j$ represents the start of the study for subject $j$.

(ii) Interval censoring: when the phenomenon of interest occurs within a finite 