Juan F. Olivares-Pacheco

Multiple constraint and truncated skew models

Attention is focussed on a truncated version of the extended two-piece skew-normal distribution, studied by Arnold et al. [On multiple constraint skewed models. Statistics. 2009;3(3):279–293]. When the truncation point is set equal to zero, the resulting model can be viewed as a flexible extension of the half-normal model. Properties of the truncated distribution are investigated and corresponding likelihood inference is considered. The methodology is applied to data set involving non-negative observations and it is verified that the fit of the truncated model compares favourably with that of the half-normal.

A New Class of Non Negative Distributions Generated by Symmetric Distributions

In this article, we study a new class of non negative distributions generated by the symmetric distributions around zero. For the special case of the distribution generated using the normal distribution, properties like moments generating function, stochastic representation, reliability connections, and inference aspects using methods of moments and maximum likelihood are studied. Moreover, a real data set is analyzed, illustrating the fact that good fits can result.

Robust modeling using the generalized epsilon-skew- t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

An Asymmetric Extension for the Family of Elliptical Slash Distributions

In this article, we introduce an asymmetric extension to the univariate slash-elliptical family of distributions studied in Gómez et al. (2007a). This new family results from a scale mixture between the epsilon-skew-symmetric family of distributions and the uniform distribution. A general expression is presented for the density with special cases such as the normal, Cauchy, Student-t, and Pearson type II distributions. Some special properties and moments are also investigated. Results of two real data sets applications are also reported, illustrating the fact that the family introduced can be useful in practice.