Scale mixtures of skew-normal-Cauchy distributions

Kahrari, Fereshte; Arellano–Valle, Reinaldo B.; Rezaei, Mehran; Yousefzadeh, Fatemeh

doi:10.1016/j.spl.2017.02.027

Cited by 10 publications

(4 citation statements)

References 7 publications

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“…The multivariate skew normal (SN) distribution has become a widely used model for regulating asymmetry departures from normality. Its study has originated fruitful research [25][26][27][28][29][30] with incremental works pursuing its enrichment and extension to wider classes of distributions [31][32][33][34][35][36][37][38][39]. This paper adopts the formulation from previous work [25,40] to define the density function of a p-dimensional SN vector with location vector ξ = (ξ 1 , .…”

Section: The Skew Normal and The Scale Mixtures Of Skew Normal Distri...mentioning

confidence: 99%

Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

Arevalillo

Navarro

2021

Symmetry

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This paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model; they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice.

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Section: The Skew Normal and The Scale Mixtures Of Skew Normal Distri...mentioning

confidence: 99%

Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

Arevalillo

Navarro

2021

Symmetry

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“…Kahrari et al [22] developed a multivariate skew-normal-Cauchy distribution and represented it as a shape mixture of the multivariate skew-normal distribution. Kahrari et al [23] modified the multivariate skew-normal-Cauchy distribution and the modified version becomes a shape mixture of a special case of the fundamental skew-normal distribution developed by Arellano-Valle and Genton [24] with a univariate half-normal mixing distribution. The class of scale mixtures of skew-normal-Cauchy distributions has been represented as a shape mixture of the class of scale mixtures of skew-normal distributions with a univariate half-normal mixing distribution [23].…”

Section: Introductionmentioning

confidence: 99%

“…Kahrari et al [23] modified the multivariate skew-normal-Cauchy distribution and the modified version becomes a shape mixture of a special case of the fundamental skew-normal distribution developed by Arellano-Valle and Genton [24] with a univariate half-normal mixing distribution. The class of scale mixtures of skew-normal-Cauchy distributions has been represented as a shape mixture of the class of scale mixtures of skew-normal distributions with a univariate half-normal mixing distribution [23]. Jamalizadeh and Lin [25] presented the scale-shape mixtures of skew-normal distributions for modeling asymmetric data.…”

Section: Introductionmentioning

confidence: 99%

Model-based computed tomography image estimation: partitioning approach

Bayisa

2019

Journal of Applied Statistics

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There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. The existing model-based methods perform poorly on bone tissues. This paper was aimed at obtaining improved bone tissue estimation. Skew-Gaussian mixture model and Gaussian mixture model were proposed to investigate CT image estimation from MR images by partitioning the data into two major tissue types. The performance of the proposed models was evaluated using leave-one-out cross-validation method on real data. In comparison with the existing model-based approaches, the model-based partitioning approach outperformed in bone tissue estimation, especially in dense bone tissue estimation.

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“…In this section, we introduce the SSMSN family of multivariate skewed distributions which is obtained as scale and shape/skewness mixtures of the multivariate SN distribution. The SSMSN family contains as special cases the SMSN class, hence also the asymmetric SNGH and symmetric SMN classes, the SHMSN, SSMN, and also the scale mixtures of skew-Normal-Cauchy distributions considered recently by [25]. For a better understanding of the new SSMSN family, we start recalling the definitions of the SMSN and SHMSN classes of distributions.…”

Section: Introductionmentioning

confidence: 99%

Scale and shape mixtures of multivariate skew-normal distributions

Arellano–Valle

Ferreira

Genton

2018

Journal of Multivariate Analysis

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We introduce a broad and flexible class of multivariate distributions obtained by both scale and shape mixtures of multivariate skew-normal distributions. We present the probabilistic properties of this family of distributions in detail and lay down the theoretical foundations for subsequent inference with this model. In particular, we study linear transformations, marginal distributions, selection representations, stochastic representations and hierarchical representations. We also describe an EMtype algorithm for maximum likelihood estimation of the parameters of the model and demonstrate its implementation on a wind dataset. Our family of multivariate distributions unifies and extends many existing models of the literature that can be seen as submodels of our proposal.

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Scale mixtures of skew-normal-Cauchy distributions

Cited by 10 publications

References 7 publications

Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

Model-based computed tomography image estimation: partitioning approach

Scale and shape mixtures of multivariate skew-normal distributions

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