Browsing by Author "Gomez, Hector W."

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    A new family of slash-distributions with elliptical contours
    (ELSEVIER SCIENCE BV, 2007) Gomez, Hector W.; Quintana, Fernando A.; Torres, Francisco J.
    We introduce a new family of univariate and multivariate slash-distributions. Our construction is based on elliptical distributions. We define the new family by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power,of a U(0, 1) random variable. The same idea is extended to the multivariate case. We study general properties of the resulting families, including their moments. We illustrate special cases of interest, such as Normal, Cauchy, Student-t, Type II Pearson and Kotz-type distributions. (c) 2007 Elsevier B.V. All rights reserved.
  • Thumbnail Image
    Item
    An Extension of the Epsilon-Skew-Normal Distribution
    (TAYLOR & FRANCIS INC, 2010) Arellano Valle, Reinaldo B.; Cortes, Milton A.; Gomez, Hector W.
    This article is related with the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000), which considers an additional shape parameter in order to increase the flexibility of the ESN distribution. Also, this article concerns likelihood inference about the parameters of the new class. In particular, the information matrix of the maximum likelihood estimators is obtained, showing that it is non singular in the special normal case. Finally, the statistical methods are illustrated with two examples based on real datasets.
  • Thumbnail Image
    Item
    Bayesian Inference for Shape Mixtures of Skewed Distributions, with Application to Regression Analysis
    (INT SOC BAYESIAN ANALYSIS, 2008) Arellano Valle, Reinaldo B.; Castro, Luis M.; Genton, Marc G.; Gomez, Hector W.
    We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear regression models under some special prior specifications for the model parameters. In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierarchical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.
  • Thumbnail Image
    Item
    Bayesian modeling using a class of bimodal skew-elliptical distributions
    (ELSEVIER SCIENCE BV, 2009) Elal Olivero, David; Gomez, Hector W.; Quintana, Fernando A.
    We consider Bayesian inference using an extension of the family of skew-elliptical distributions studied by Azzalini [1985. A class of distributions which includes the normal ones. Scand. J. Statist. Theory and Applications 12 (2), 171-178]. This new class is referred to as bimodal skew-elliptical (BSE) distributions. The elements of the BSE class can take quite different forms. In particular, they can adopt both uni- and bimodal shapes. The bimodal case behaves similarly to mixtures of two symmetric distributions and we compare inference under the BSE family with the specific case of mixtures of two normal distributions. We study the main properties of the general class and illustrate its applications to two problems involving density estimation and linear regression. (C) 2008 Elsevier B.V. All rights reserved.