Family of multivariate generalized t distributions

Arslan, Olçay

doi:10.1016/j.jmva.2003.09.008

Cited by 30 publications

(26 citation statements)

References 9 publications

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“…Similarly, matricvariate versions of the results in Arslan (2004Arslan ( , 2005, Haro-López and Smith (1999) and ArellanoValle and Bolfarine (1995) are obtained.…”

Section: Compound Kotz-type Distribution Of a Random Matrixmentioning

confidence: 94%

“…Arslan (2005) proposed the scale mixture of the vector variate Kotz-type distribution, also termed the t-type or generalised t distribution. These latter two names are used because Arslan (2005) generalised the multivariate t distribution and the generalised version of the multivariate t distribution proposed by Arellano-Valle and Bolfarine (1995) and Arslan (2004).…”

Section: Introductionmentioning

confidence: 99%

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Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions

Dı́az-Garcı́a

Jáimez

2010

Journal of the Korean Statistical Society

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a b s t r a c tWe have derived the generalised Wishart and inverse-Wishart distributions based on the matrix variate and matricvariate Kotz-type distributions. The scale mixture of matricvariate and matrix variate Kotz-type distributions and the inverse generalised gamma distribution are then proposed. It is shown that the class of distributions termed the family of t-type distributions proposed by Arslan [Arslan, O. (2005). A new class of multivariate distributions: Scale mixture of Kotz-type distributions. Statistics and Probability Letters, 76, 18-28] is obtained as particular cases of the result given here. We have also derived the compound matricvariate and matrix variate Kotz-type distributions and the inverse generalised Wishart based on the matrix variate and matricvariate Kotztype distributions. These latter results lead us to propose a different matricvariate version of the family of t-type distributions and others cited in the above-mentioned reference.

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“…Similarly, matricvariate versions of the results in Arslan (2004Arslan ( , 2005, Haro-López and Smith (1999) and ArellanoValle and Bolfarine (1995) are obtained.…”

Section: Compound Kotz-type Distribution Of a Random Matrixmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions

Dı́az-Garcı́a

Jáimez

2010

Journal of the Korean Statistical Society

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“…Let X be a d-dimensional random vector with an MGT (µ, Σ, λ, β, q) distribution (see Arslan (2004) for details). The density function of X is…”

Section: The Gt-copulamentioning

confidence: 99%

“…Although the parameters β and q play similar roles, the parameter β has larger influence on the density shape and affects the kurtosis. More information on the MGt distribution can be found in Arslan (2004).…”

Section: The Gt-copulamentioning

confidence: 99%

“…The GT family applies to symmetric, fat-tailed data and therefore adjusts for the leptokurtosis of nonnormal data. Recently, Theodossiou (1998) introduced the univariate skew GT Distribution and Arslan (2004) defined a new family of multivariate generalized t (MGT) distributions. The MGT family includes as special cases the multivariate t distribution, and the generalized t distribution defined by Arellano-Valle and Bolfarine (1995).…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Skew Distributions Based on the GT-Copula

Mendes

Arslan

2006

Brazilian Review of Econometrics

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In this paper we obtain the expression for the copula pertaining to the multivariate generalized t distribution, the generalized t-copula, or in short, GT-copula. The GT-copula generalizes some well known copulas, such as the one associated with the multivariate t distribution (t-copula). We derive the expression for its tail dependence coefficient and show that the GT-copula may adjust for stronger tail dependence when compared to the t-copula. The potentiality of the GT-copula allows for modeling varying degrees and different types (linear and nonlinear) of dependence, as well as multimodality. By applying Sklar's theorem to the GT-copula, and by mixing symmetric and asymmetric margins, we construct a new family of multivariate distributions. The resulting distributions are suitable for modeling a wide variety of skew datasets. The flexibility of the copula approach suggests applications in many fields, such as environment and finance. We provide an illustration, where we quantify stock market linkages.

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An adaptive kriging method for solving nonlinear inverse statistical problems

Fu¹,

Couplet²,

Bousquet

2017

Environmetrics

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In various environmental contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi)+Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is implemented by a CPU‐consuming computer model H, a major practical difficulty is to perform the statistical inference with a relatively small number of runs of H. A Bayesian statistical framework is considered to make use of possible prior knowledge on the parameters of the distribution of the Xi, which is assumed Gaussian. Moreover, a Markov Chain Monte Carlo algorithm is carried out to estimate their posterior distribution by replacing H by a kriging metamodel build from a limited number of simulated experiments. Two heuristics, involving two different criteria to be optimized, are proposed to sequentially design these computer experiments in the limits of a given computational budget. The first criterion is a weighted integrated mean square error. The second one, called expected conditional divergence, developed in the spirit of the stepwise uncertainty reduction criterion is based on the discrepancy between two consecutive approximations of the target posterior distribution. Several numerical comparisons conducted over a toy example then a motivating hydraulic real case study show that such adaptive designs can significantly outperform the classical choice of a maximin latin hypercube design of experiments. Dealing with a major concern in hydraulic engineering, a particular emphasis is placed upon the prior elicitation of the case study, highlighting the overall feasibility of the methodology. Faster convergences and manageability considerations lead to recommend the use of the expected conditional divergence criterion in practical applications.

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Family of multivariate generalized t distributions

Cited by 30 publications

References 9 publications

Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions

Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions

Multivariate Skew Distributions Based on the GT-Copula

An adaptive kriging method for solving nonlinear inverse statistical problems

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