Statistical Applications of the Multivariate Skew Normal Distribution

Azzalini, Adelchi; Capitanio, Antonella

doi:10.1111/1467-9868.00194

Cited by 1,100 publications

(829 citation statements)

References 24 publications

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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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“…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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“…vector representing the l th derivative of the trajectory at T (e.g., P (0) , P (1) , and P (2) are, respectively, a d-dimensional location, velocity, and acceleration at T); o T is a specific time point at which the above state was observed (or sensed); o For all l=0,..,k-1, IME (l) is the domain of possible instrument-and-measurement errors (deviations from the real) associated with P (l) .…”

Section: Definition 1 Database Trajectorymentioning

confidence: 99%

“…For example, for an application wherein sensors can detect and report only the 3-dimensional geographic location of the object each time, d is set to 3 and k is set to 1. If the sensors can report not only locations but also velocities (i.e., P (1) ), k is set to 2.…”

Section: Definition 1 Database Trajectorymentioning

confidence: 99%

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The Tornado Model: Uncertainty Model for Continuously Changing Data

Kim

Alkobaisi

et al.

Advances in Databases: Concepts, Systems and Applications

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Abstract.To support emerging database applications that deal with continuously changing (or moving) data objects (CCDO), such as vehicles, RFIDs, and multi-stimuli sensors, one requires an efficient data management system that can store, update, and retrieve large sets of CCDOs. Although actual CCDOs can continuously change over time, computer systems cannot deal with continuously occurring infinitesimal changes. Thus, in the data management system, each object's spatiotemporal values are associated with a certain degree of uncertainty at virtually every point in time, and the queries are mostly processed over estimates characterizing the uncertainty. The smaller the uncertainty is, the better the query performance becomes. The paper proposes a sophisticated asymmetric uncertainty model, called the Tornado Model, which can effectively represent, process, and minimize the data uncertainty for a wide variety of CCDO database applications.

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Statistical Applications of the Multivariate Skew Normal Distribution

Cited by 1,100 publications

References 24 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

The Tornado Model: Uncertainty Model for Continuously Changing Data

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