the density and hazard functions obtained for a log two-piece sinh-arcsinh distribution (LTP SAS, which is obtained by using a symmetric sinh-arcsinh baseline density function in (\[TP2\]), see also [@R15]. The corresponding expression is provided in Appendix A). The implementation of LTP distributions is straightforward in R by using the packages ‘twopiece’ and ‘TPSAS’, which are freely available upon request. Moreover, the $p$th moment of a LTP distribution exists, whenever the $p$th moment of the underlying (log-symmetric) log-$s$ distribution exists. In particular, all moments of the LTP normal distribution exist.

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An alternative construction {#an-alternative-construction .unnumbered}
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The family of two-piece distributions (\[TP\])-(\[TP2\]) can be seen as a special kind of finite mixtures of truncated PDFs, as shown in [@RS14]. In a similar fashion, the family of log two-piece distributions can be obtained as a particular class of finite mixtures of truncated distributions with positive support. In the context of survival and size distributions these sorts of mixtures are known as composite models (see [@NB13] for a literature review). Recall first that the PDF of a composite model can be written as: $$\begin{aligned}
\label{CompPDF}
s_c(y) 