Discrete mixture models are one of the most successful approaches for
density estimation. Under a Bayesian nonparametric framework, Dirichlet process
location–scale mixture of Gaussian kernels is the golden standard, both having nice
theoretical properties and computational tractability. In this paper we explore the use of
the skew-normal kernel, which can naturally accommodate several degrees of skew-
ness by the use of a third parameter. The choice of this kernel function allows us
to formulate nonparametric location–scale–shape mixture prior with desirable the-
oretical properties and good performance in different applications. Efficient Gibbs
sampling algorithms are also discussed and the performance of the methods are tested
through simulations and applications to galaxy velocity and fertility data. Extensions
to accommodate discrete data are also discussed.

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• Bayesian nonparametric location–scale–shape mixtures