On the Unification of Families of Skew‐normal Distributions

By Reinaldo Boris Arellano-Valle, Adelchi Azzalini. 2006

396 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a9f4096ece4446bf47063ab67195a3b5692bf68c

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Skew Brownian Motion and Pricing European Options (2007, methodology): “The density of X t can be derived using the results found in Arellano Valle and Azzalini ( 2006 ), since W 1, t and W 2, t are independently normally distributed with zero mean and variance t ; the density of X t is given by”
Multivariate log‐skew‐elliptical distributions with applications to precipitation data (2009, background): “To present a conditional distribution of X2|X1 for a log-skew-elliptical random vector X, we first need to define the so-called extended skew-elliptical family (Arellano-Valle and Genton, 2009; Arellano-Valle and Azzalini, 2006; Arellano-Valle et al., 2006).”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, methodology): “In other words, this representation allows to identify the function w(z) within the class defined by (1) when f = φ and G = Φ.”
Lambert W random variables—a new family of generalized skewed distributions with applications to risk estimation (2009, positive): “This approach to skewness has not only led to substantial research in the skewnormal case [Azzalini and Capitanio (1999), Arellano-Valle and Azzalini (2006)], but the same concept has also been used for student-t [Azzalini and Capitanio (2003)] and Cauchy distributions [Arnold and Beaver (2000), Beh”
The centred parametrization for the multivariate skew-normal distribution (2008, background): “This parametrization is not really of direct statistical use as it lacks a simple meaningful interpretation, for the reasons explained by Arellano-Valle and Azzalini [1], but it proves to be a useful technical device.”
Multivariate stochastic volatility (2009, background): “Other multivariate skew densities have also been proposed, for example, in Arellano-Valle and Azzalini (2006) , Bauwens and Laurent (2005), Dey and Liu (2005) Azzalini (2005), Gupta et al. (2004) and Ferreira and Steel (2004).”
LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS (2010, neutral): “…by using the well known stochastic representation Y d = µ+ δZ(−c̄,∞) +Z, where Z(−c̄,∞) d = (Z0|Z0 + c̄ > 0), with Z0 ∼ N(0, 1) and being independent of Z ∼ Np(0,Σ−δδ⊤) (see e.g. Arellano-Valle and Azzalini, 2006), and the fact that E{Z(−c̄,∞)} = WΦ1 (c̄) (see Johnson et al., 1994, Section 10.1).”
A Heckman Selection-t Model (2012, background): “, Fang, Kotz, and Ng 1990), then Y ∗|U ∗ > 0 has an extended skew-elliptical distribution (Arellano-Valle and Azzalini 2006; Arellano-Valle and Genton 2010b).”
A unified view on skewed distributions arising from selections (2006, methodology): “In fact, with some modification of the parameterization used by Arellano-Valle & Azzalini (2006), theSUEpdf is just the selection pdf that follows from (7) withC = C(0) and has the form fX(x) = fp(x; ξV,ΩV, h (p)) Fq(ξU + ∆ ⊤Ω−1 V (x − ξ V );0,ΩU − ∆ ⊤Ω−1 V ∆, h (q) υ(x)) Fq(ξU;0,ΩU, h (q)) ,…”
Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes (2015, methodology): “We consider a general class of skew normal distributions that was originally proposed in Arellano-Valle and Azzalini (2006) and present it here in a particularly useful way for the context of our work.”
Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions (2013, background): “On the other hand, since (see, e.g., Arellano-Valle & Azzalini, 2006; Arellano-Valle et al., 2006a) Zc d= ̄|X0|+ (Ik − ̄̄T )1/2X, where ̄= ̄√ 1+‖̄‖2 and ( X X0 ) ∼ECk +1 (( 0 0 ) , ( Ik 0 0T 1 ) , h(k +1) ) , we have W d=‖̄‖|X0|+ √ 1−‖̄‖2X1, where X1 = T X∼EC1(0, 1, h(1)) is distributed as the…”