On fundamental skew distributions

Arellano–Valle, Reinaldo B.; Genton, Marc G.

doi:10.1016/j.jmva.2004.10.002

Cited by 307 publications

(254 citation statements)

References 22 publications

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“…The SU E distribution was also considered in Arellano-Valle and Azzalini (2006) with a different but equivalent parameterization, see also and Arellano-Valle and Genton (2005). However, these authors did not study systematically the main properties of the SU E distributions, for instance such as marginal and conditional distributions, and moments.…”

Section: Distribution Denoted Bymentioning

confidence: 99%

Multivariate extended skew-t distributions and related families

Arellano–Valle

Genton

2010

METRON

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SummaryA class of multivariate extended skew-t (EST ) distributions is introduced and studied in detail, along with closely related families such as the subclass of extended skew-normal distributions. Besides mathematical tractability and modeling flexibility in terms of both skewness and heavier tails than the normal distribution, the most relevant properties of the EST distribution include closure under conditioning and ability to model lighter tails as well. The first part of the present paper examines probabilistic properties of the EST distribution, such as various stochastic representations, marginal and conditional distributions, linear transformations, moments and in particular Mardia's measures of multivariate skewness and kurtosis. The second part of the paper studies statistical properties of the EST distribution, such as likelihood inference, behavior of the profile log-likelihood, the score vector and the Fisher information matrix. Especially, unlike the extended skew-normal distribution, the Fisher information matrix of the univariate EST distribution is shown to be non-singular when the skewness is set to zero. Finally, a numerical application of the conditional EST distribution is presented in the context of confidential data perturbation.

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Section: Distribution Denoted Bymentioning

confidence: 99%

Multivariate extended skew-t distributions and related families

Arellano–Valle

Genton

2010

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“…The publication of initial papers by Branco and Dey (2001), Azzalini and Capitanio (2003) and Sahu et al (2003) has been followed by articles by several authors including Arellano-Valle and Genton (2005), Arrellano-Valle et al (2006), Arrellano-Valle and Azzalini (2006) and Azzalini and Genton (2008). An extended skew Student distribution and many of its properties are described in Arellano-Valle and Genton (2008), henceforth AV&G.…”

Section: Introductionmentioning

confidence: 99%

Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution

Adcock

2009

Ann Oper Res

122

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The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar meanvariance frontier, and which may be implemented using quadratic programming.

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“…Here, we utilize the multivariate SN and ST distributions introduced by Sahu et al [32] and extended by others (ArellanoValle and Genton, [33]). We also make use of the multivariate Laplace distribution and its skewed version proposed by Arslan [34].…”

Section: Multivariate Se Distributionsmentioning

confidence: 99%

Bayesian Analysis of Joint Modeling of Longitudinal and Time to Event Data Using Some Skew-Elliptical Distributions

Khoundabi¹,

Kazemnejad²,

Mansourian³

et al. 2017

BBIJ

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Joint modeling of longitudinal and time to event data have been widely used for analyzing medical data, where longitudinal measurements is gathered with a time to event or survival data. In most of these studies, distributional assumption for modeling longitudinal response is normal, which leads to vulnerable inference in the presence of outliers in longitudinal measurements and violation of this assumption. Violation of the normality assumption can also make the statistical inference vague. Powerful distributions for robust analyzing and relaxing normality assumption, are skew-elliptical distributions, which include univariate and multivariate versions of the student's t, the Laplace and normal distributions. In this paper, a linear mixed effects model with skew-elliptical distribution for both random effects and residuals and a Cox's model for time to event data are used for joint modeling. This strategy allows for the skewness and the heavy tails of random effect distributions and thus makes inferences robust to the violation. For estimation, a Bayesian parametric approach using Markov chain Monte Carlo is adopted. The method is illustrated in a real Intensive Care Unit (ICU) data set and the best model is selected using some Bayesian criteria for model selection.

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On fundamental skew distributions

Cited by 307 publications

References 22 publications

Multivariate extended skew-t distributions and related families

Multivariate extended skew-t distributions and related families

Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution

Bayesian Analysis of Joint Modeling of Longitudinal and Time to Event Data Using Some Skew-Elliptical Distributions

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