  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 skewness by the use of a third parameter. The choice of this
kernel function allows us to formulate nonparametric location-scale-shape
mixture prior with large support and good performance in different
applications. Asymptotically, we show that this modelling framework is
consistent in frequentist sense. 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.
