The multivariate skew-normal distribution

Azzalini, Adelchi; Capitanio, Antonella

doi:10.1017/cbo9781139248891.006

Cited by 298 publications

(524 citation statements)

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“…Of course, for δ = 0 we have the Gaussian case. For a detailed study of the skew-Gaussian distribution, we refer the reader to Azzalini (1985Azzalini ( , 1986, Azzalini and Dalla Valle (1996), Azzalini and Capitanio (1999), Arellano-Valle and Azzalini (2006) and Azzalini (2013).…”

Section: Skew-gaussian Rfs On the Unit Spherementioning

confidence: 99%

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

et al. 2017

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This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in R 3 , allowing for modeling data available over large portions of planet Earth. This model admits explicit expressions for the marginal and cross covariances. However, the n-dimensional distributions of the field are difficult to evaluate, because it requires the sum of 2 n terms involving the cumulative and probability density functions of a n-dimensional Gaussian distribution. Since in this case inference based on the full likelihood is computationally unfeasible, we propose a composite likelihood approach based on pairs of spatial observations. This last being possible thanks to the fact that we have a closed form expression for the bivariate distribution. We illustrate the effectiveness of the method through simulation experiments and the analysis of a real data set of minimum and maximum surface air temperatures.

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Section: Skew-gaussian Rfs On the Unit Spherementioning

confidence: 99%

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

et al. 2017

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“…All of these share several properties similar to the multivariate normal distribution. In this paper, we select the multivariate skew distribution version originally proposed by Azzalini and Dalla Valle (1996) for a number of reasons. This version is efficient in the number of additional parameters to be estimated, allows independence between skewnormally distributed and normally-distributed elements in a multivariate vector (useful in selectively imposing skew-normality only on certain coefficients), is closed under any affine transformation of the skew-normally distributed vector (is the key to the MACML estimation of the MNP model), and is closed under the sum of independent skew-normally distributed and normally distributed vectors of the same dimensions (is the key to non-normally mixing distributions superimposed on an MNP kernel).…”

Section: The Multivariate Skew-normal Distribution Functionmentioning

confidence: 99%

“…Specifically, we introduce the use of a multivariate skew-normal distribution function for mixing with an MNP kernel model. The skew-normal distribution, considered by O'Hagan and Leonard (1976) and formalized by Azzalini (1985) for the univariate case, has been extended to the multivariate case by Azzalini and Dalla Valle (1996) and Azzalini and Capitanio (1999).…”

Section: Introductionmentioning

confidence: 99%

A new approach to specify and estimate non-normally mixed multinomial probit models

Bhat

Sidharthan

2012

Transportation Research Part B: Methodological

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The current paper proposes the use of the multivariate skew-normal distribution function to accommodate non-normal mixing in cross-sectional and panel multinomial probit (MNP) models. The combination of skew-normal mixing and the MNP kernel lends itself nicely to estimation using Bhat's (2011) maximum approximate composite marginal likelihood (MACML) approach. Simulation results for the cross-sectional case show that our proposed approach does well in recovering the underlying parameters, and also highlights the pitfalls of ignoring non-normality of the continuous mixing distribution when such non-normality is present. At the same time, the proposed model obviates the need to assume a pre-specified parametric distribution for the mixing, and allows the estimation of a very flexible, but still parsimonious, mixing distribution form.

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“…Ali and Woo (2006) and Woo (2006) studied several skew -symmetric reflected distributions, which do not include some reflected distributions. Azzalini and Capitanio (1999) studied the multivariate skewed normal distribution and Woo (2007) studied the reliability in a half-triangle distribution and a skewed distribution. Balakrishnan and Cohen (1991) proposed the method of finding an approximate MLE for the scale parameter in several distributions.…”

Section: Introductionmentioning

confidence: 99%

Estimations of the skew parameter in a skewed double power function distribution

Kang¹,

Lee²

2013

Journal of the Korean Data and Information Science Society

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A skewed double power function distribution is defined by a double power function distribution. We shall evaluate the coefficient of the skewness of a skewed double power function distribution. We shall obtain an approximate maximum likelihood estimator (MLE) and a moment estimator (MME) of the skew parameter in the skewed double power function distribution, and compare simulated mean squared errors for those estimators. And we shall compare simulated MSEs of two proposed reliability estimators in two independent skewed double power function distributions with different skew parameters.

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The multivariate skew-normal distribution

Cited by 298 publications

References 0 publications

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

Estimating covariance functions of multivariate skew-Gaussian random fields on the sphere

A new approach to specify and estimate non-normally mixed multinomial probit models

Estimations of the skew parameter in a skewed double power function distribution

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