Browsing by Author "Azzalini, Adelchi"

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    A formulation for continuous mixtures of multivariate normal distributions
    (ELSEVIER INC, 2021) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
    Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal variable, by changing the nature of these basic constituents from constants to random quantities. More recently, other mixture-type constructions have been introduced, where the core random component, on which the mixing operation operates, is not necessarily normal. The main aim of the present work is to show that many existing constructions can be encompassed by a formulation where normal variables are mixed using two univariate random variables. For this formulation, we derive various general properties, with focus on the multivariate context. Within the proposed framework, it is also simpler to formulate new proposals of parametric families, and we provide a few such instances. As a side product, the exposition provides a concise compendium of the main constructions of continuous normal-mixtures type, although a full overview of this vast theme is not attempted. (C) 2021 Published by Elsevier Inc.
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    On the non-identifiability of unified skew-normal distributions
    (2023) Wang, Kesen; Arellano-Valle, Reinaldo B.; Azzalini, Adelchi; Genton, Marc G.
    We investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parameterizations and extends to the family of unified skew-elliptical distributions and more generally to selection distributions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.
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    On the unification of families of skew-normal distributions
    (BLACKWELL PUBLISHING, 2006) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
    The distribution theory literature connected to the multivariate skew-normal distribution has grown rapidly in recent years, and a number of extensions and alternative formulations have been put forward. Presently there are various coexisting proposals, similar but not identical, and with rather unclear connections. The aim of this paper is to unify these proposals under a new general formulation, clarifying at the same time their relationships. The final part sketches an extension of the argument to the skew-elliptical family.
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    Some properties of the unified skew-normal distribution
    (2022) Arellano-Valle, Reinaldo B.; Azzalini, Adelchi
    For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia's measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.
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    The centred parametrization for the multivariate skew-normal distribution
    (ELSEVIER INC, 2008) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
    For statistical inference connected to the scalar skew-normal distribution, it is known that the so-called centred parametrization provides a more convenient parametrization than the one commonly employed for writing the density function. We extend the definition of the centred parametrization to the multivariate case, and study the corresponding information matrix. (C) 2008 Elsevier Inc. All rights reserved.