On the multivariate skew-normal-Cauchy distribution

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

doi:10.1016/j.spl.2016.05.005

Cited by 21 publications

(8 citation statements)

References 28 publications

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“…By Lemma 7 and (11), and Lemma 8 and (2), respectively, for the cases (25) and (27), we have X 1 + X 2 ≼ icx Y 1 + Y 2 if and only if σ X,11 + σ X,22 + 2σ X,12 ≤ σ Y,11 + σ Y,22 + 2σ X,12 . Since σ X,11 = σ Y,11 and σ X,22 = σ Y,22 , it becomes equivalent to ρ X ≤ ρ Y , as required.…”

Section: Proofmentioning

confidence: 90%

“…Shape mixture of SN distribution when a 1 = 1 and a 2 (τ ) = s(τ ). The multivariate skew-generalized-normal [3] when s(τ ) = τ ∼ N (1, a), the multivariate skew-normal-Cauchy [27] when s(τ ) = |τ | and τ ∼ N (0, 1); 3. If a 2 (τ ) = √ a 1 (τ ), then two examples are the multivariate skew-t-normal and multivariate skew-slashnormal distributions, when τ ∼ Gamma(ν/2, ν/2) and τ ∼ Beta(ν, 1), respectively [20].…”

Section: Remarkmentioning

confidence: 99%

“…, where X and Y are random vectors for both cases (25) and (27). Then, X 1 + X 2 ≼ icx Y 1 + Y 2 if and only if ρ X ≤ ρ Y .…”

Section: Propositionmentioning

confidence: 99%

See 2 more Smart Citations

Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

Jamali

Amiri

Jamalizadeh

2020

Stat., optim. inf. comput.

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‎In this paper‎, ‎we introduce integral stochastic ordering of two‎ most important classes of distributions that are commonly used to fit data possessing high values of skewness and (or)‎ ‎kurtosis‎. ‎The first one is based on the selection distributions started by the univariate skew-normal distribution‎. ‎A broad‎, ‎flexible and newest class in this area is the scale and shape mixture of multivariate skew-normal distributions‎. ‎The second one is the general class of Normal Mean-Variance Mixture distributions‎. ‎We then derive necessary and sufficient conditions for comparing the random vectors from these two classes of distributions‎. ‎The integral orders considered here are the usual‎, ‎concordance‎, ‎supermodular‎, ‎convex‎, ‎increasing convex and directionally convex stochastic orders‎. ‎Moreover‎, ‎for bivariate random vectors‎, ‎in the sense of stop-loss and bivariate concordance stochastic orders‎, ‎the dependence strength of random portfolios is characterized in terms of order of correlations‎.

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Section: Proofmentioning

confidence: 90%

Section: Remarkmentioning

confidence: 99%

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Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

Jamali

Amiri

Jamalizadeh

2020

Stat., optim. inf. comput.

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“…For η(S ) = |S | ∼ HN(0, 1), we obtain the multivariate skew-normal-Cauchy (SNC) distribution studied recently by [26].…”

Section: Special Subclasses Of Ssmsn Distributionsmentioning

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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“…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.…”

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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On the multivariate skew-normal-Cauchy distribution

Cited by 21 publications

References 28 publications

Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

Scale and shape mixtures of multivariate skew-normal distributions

Model-based computed tomography image estimation: partitioning approach

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