Some considerations and developments about recently proposed families of distributions with hinge points.

This paper deals with probability density functions with hinge points, useful when representing phenomena which have different statistical features, depending on the fact that a threshold point has been overtaken or not. The STSP distribution, proposed by Van Dorp and Kotz (2002), is recalled and developed, and a modified model (MTSP), a mixture of STSP and Uniform, is defined and studied. Moreover the Two-faced distribution, already presented in Brizzi (2006), is recalled and thoroughly analysed, and some estimation problems, related to both models considered, are faced by a semi-empirical approach. References: - J.R. Van Dorp and S.Kotz (2002), The standard two-sided power distribution and its properties, with applications to financial engineering. "The American Statistician", 56, pp. 90-99. - M.Brizzi (2006), A skewed model combining triangular and exponential features: the two-faced distribution and its statistical properties. "Austrian Journal of Statistics", 35, pp. 455-462.