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Paper No. 07-18

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FA Quintana, MFJ Steel and JTAS Ferreira

Flexible Univariate Continous Distributions

Abstract: Based on a constructive representation, which distinguishes between a skewing mechanism P and an underlying symmetric distribution F, we introduce two fexible classes of distributions. They are generated by nonparametric modelling of either P or F. We examine properties of these distributions and consider how they can help us to identify which aspects of the data are badly captured by simple symmetric distributions. Within a Bayesian framework, we investigate useful prior settings and conduct inference through MCMC methods. On the basis of simulated and real data examples, we make recommendations for the use of our models in practice.

Keywords: density estimation; location-scale; modal regression; moment existence; skewness; unimodality.