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The smooth piecewise-linear models cover a wide range of applicationsnowadays. Basically, there are two classes of them: models are transitional orhyperbolic according to their behaviour at the phase-transition zones. Thisstudy explored three different approaches to build smooth piecewise-linearmodels, and we analysed their inter-relationships by a unifying modellingframework. We conceived the smoothed phase-transition zones as domains where amixture process takes place, which ensured probabilistic interpretations forboth hyperbolic and transitional models in the light of random thresholds. Manypopular models found in the literature are special cases of our methodology.Furthermore, this study introduces novel regression models as alternatives,such as the Epanechnikov, Normal and Skewed-Normal Bent-Cables.

A family of smooth piecewise-linear models with probabilistic interpretations