Browsing by Author "Gomez, Hector W."

Now showing 1 - 7 of 7
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    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.
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    An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations
    (2022) Arrue, Jaime; Arellano-Valle, Reinaldo Boris; Venegas, Osvaldo; Bolfarine, Heleno; Gomez, Hector W.
    In this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such as the computation of its moments and the non-existence of the moment-generating function. Parameter estimation by the maximum likelihood approach is also studied. This approach presents an overestimation problem in the shape parameter, which in some cases, can even be infinite. However, as we demonstrate, this problem is solved by adapting bias reduction using Firth's approach. We also show that the modified log-skew-normal model likewise inherits the non-singularity of the Fisher information matrix of the untransformed model, when the shape parameter is null. Finally, we apply the modified log-skew-normal model to a real example related to pollution data.
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    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.
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    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.
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    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.
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    Likelihood Based Inference and Bias Reduction in the Modified Skew-t-Normal Distribution
    (2023) Arrue, Jaime; Arellano-Valle, Reinaldo B.; Calderin-Ojeda, Enrique; Venegas, Osvaldo; Gomez, Hector W.
    In this paper, likelihood-based inference and bias correction based on Firth's approach are developed in the modified skew-t-normal (MStN) distribution. The latter model exhibits a greater flexibility than the modified skew-normal (MSN) distribution since it is able to model heavily skewed data and thick tails. In addition, the tails are controlled by the shape parameter and the degrees of freedom. We provide the density of this new distribution and present some of its more important properties including a general expression for the moments. The Fisher's information matrix together with the observed matrix associated with the log-likelihood are also given. Furthermore, the non-singularity of the Fisher's information matrix for the MStN model is demonstrated when the shape parameter is zero. As the MStN model presents an inferential problem in the shape parameter, Firth's method for bias reduction was applied for the scalar case and for the location and scale case.
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    On a new type of Birnbaum-Saunders models and its inference and application to fatigue data
    (2020) Arrue, Jaime; Arellano-Valle, Reinaldo B.; Gomez, Hector W.; Leiva, Victor
    The Birnbaum-Saunders distribution is a widely studied model with diverse applications. Its origins are in the modeling of lifetimes associated with material fatigue. By using a motivating example, we show that, even when lifetime data related to fatigue are modeled, the Birnbaum-Saunders distribution can be unsuitable to fit these data in the distribution tails. Based on the nice properties of the Birnbaum-Saunders model, in this work, we use a modified skew-normal distribution to construct such a model. This allows us to obtain flexibility in skewness and kurtosis, which is controlled by a shape parameter. We provide a mathematical characterization of this new type of Birnbaum-Saunders distribution and then its statistical characterization is derived by using the maximum-likelihood method, including the associated information matrices. In order to improve the inferential performance, we correct the bias of the corresponding estimators, which is supported by a simulation study. To conclude our investigation, we retake the motivating example based on fatigue life data to show the good agreement between the new type of Birnbaum-Saunders distribution proposed in this work and the data, reporting its potential applications.