Multivariate T-Distributions and Their Applications

Kotz, Samuel; Nadarajah, Saralees

doi:10.1017/cbo9780511550683

Cited by 670 publications

(366 citation statements)

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“…(1) Note that in this standard parameterization ÓÚº » ¾ so that the covariance matrix is not equal to and is in fact only defined if ¾. A useful recent reference for the multivariate t is Kotz & Nadarajah (2004).…”

Section: The Multivariate T Distributionmentioning

confidence: 99%

“…A special, but little-studied, case of this family is encountered when W Igº ¾ ¾» (since inverse gamma is a special case of the GIG distribution). The resulting mixture distribution could be referred to as a skewed multivariate t (although there are a number of other multivariate distributions sharing this name; see Kotz & Nadarajah (2004)) and has density…”

Section: Skewed T Copulamentioning

confidence: 99%

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The t Copula and Related Copulas

Demarta¹,

McNeil²

2007

International Statistical Review

774

470

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The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.

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Section: The Multivariate T Distributionmentioning

confidence: 99%

Section: Skewed T Copulamentioning

confidence: 99%

The t Copula and Related Copulas

Demarta¹,

McNeil²

2007

International Statistical Review

774

470

View full text Add to dashboard Cite

show abstract

“…Under the null hypothesis, D 0 and D 0 , and Q y D 1=2 .y / and Q y 0 D 1=2 .y 0 / yield two uncorrelated samples. These two uncorrelated samples both follow N.0; 1/ if F is n-variate normal, and both follow the central t distribution if F is n-variate t with degrees of freedom > 2 (see Kotz and Nadarajah, 2004). Note and can be replaced by 0 and 0 in computing Q y and Q y 0 .…”

Section: Hypothesis Testingmentioning

confidence: 99%

Defining spatial comparison metrics for evaluation of paleoclimatic field reconstructions of the Common Era

Smerdon

2012

Environmetrics

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Climate field reconstructions (CFR) of the Common Era (the last two millennia) provide important insights into the dynamics of past climate change that, in turn, have implications for the future. Multiple CFR methods have emerged in the literature, and comparisons between these methods using pseudoproxy experiments have been performed. These experiments, however, have not fully quantified the spatial skill of the CFRs, particularly with regard to the relative performance of each. Toward such ends, a formal statistical hypothesis test is proposed as a means of evaluating the differences between two random fields that integrate the differences in both the mean and the dependence structure. This involves a careful selection of the statistical model for the CFR residual process and systematic comparisons over different spatial scales. Application of this method yields a systematic assessment of the spatial character of five widely applied CFRs in a pseudoproxy experiment context. The analyses indicate that spatial differences among the five CFRs are not statistically significant. Further rigorous statistical assessments will help elucidate the strength and weakness of each CFR method, while quantifying the degree to which their spatial dissimilarities can be ascribed to methodological choices. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Also, since the charts are proposed for use with data that are not assumed to follow a certain distribution (such as the normal distribution) it is important to consider some non-normal situations for what-if analysis. A commonly used non-multivariate normal distribution in the literature that will be used for the simulation is the multivariate t distribution (see Cherubini et al [30], Kotz and Nadarajah [31], and Johnson and Kotz [32]).…”

Section: Performance Studymentioning

confidence: 99%

Two simple Shewhart‐type multivariate nonparametric control charts

Boone¹,

Chakraborti²

2011

Appl Stoch Models Bus & Ind

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In many quality control applications, the necessary distributional assumptions to correctly apply the traditional parametric control charts are either not met or there is simply no enough information or evidence to verify the assumptions. It is well known that the performance of many parametric control charts can be seriously degraded in situations like this. Thus, control charts that do not require a specific distributional assumption to be valid, the so‐called nonparametric or distribution‐free charts, are desirable in practice. In this paper, two simple to use multivariate nonparametric control charts are considered. The charts are Shewhart‐type charts and are based on the multivariate forms of the sign and the Wilcoxon signed‐rank tests. The performance of the proposed charts is studied in a simulation study. Some observations and recommendations are made. Copyright © 2011 John Wiley & Sons, Ltd.

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Multivariate T-Distributions and Their Applications

Cited by 670 publications

References 0 publications

The t Copula and Related Copulas

The t Copula and Related Copulas

Defining spatial comparison metrics for evaluation of paleoclimatic field reconstructions of the Common Era

Two simple Shewhart‐type multivariate nonparametric control charts

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