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Paper No. 13-10

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FJ Rubio and MFJ Steel

Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations

Abstract: In this paper we introduce the double two-piece transformation defined on the family of unimodal symmetric continuous distributions containing a shape parameter. The distributions obtained with this transformation contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of transformations are presented. We propose interpretable scale and location invariant benchmark priors and derive conditions for the existence of the corresponding posterior distribution. Finally, we conduct inference with these models using three realdata examples.

Keywords: kurtosis; posterior existence; scale mixtures of normals; skewness; Student-t distribution; unimodal continuous distributions.