Browsing by Author "Gomez, HW"

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    A new class of skew-normal distributions
    (TAYLOR & FRANCIS INC, 2004) Arellano Valle, RB; Gomez, HW; Quintana, FA
    We introduce a new family of asymmetric normal distributions that contains Azzalini's skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.
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    Statistical inference for a general class of asymmetric distributions
    (ELSEVIER SCIENCE BV, 2005) Arellano Valle, RB; Gomez, HW; Quintana, FA
    We consider a general class of asymmetric univariate distributions depending on a real-valued parameter a, which includes the entire family of univariate symmetric distributions as a special case. We discuss the connections between our proposal and other families of skew distributions that have been studied in the statistical literature. A key element in the construction of such families of distributions is that they can be stochastically represented as the product of two independent random variables. From this representation we can readily derive theoretical properties, easy-to-implement simulation schemes as well as extensions to the multivariate case. We also study statistical inference for this class based on the method of moments and maximum likelihood. We give special attention to the skew-power exponential distribution, but other cases like the skew-t distribution are also considered. Finally, the statistical methods are illustrated with 3 examples based on real datasets. (C) 2004 Elsevier B.V. All rights reserved.