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Abstract:
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A random vector $X$ is a normal mean-variance mixture provided $X$, for a given $W \geq 0$, follows a multivariate normal distribution with mean vector $\mu + \beta W$ and covariance matrix $W\Sigma$, and provided $W$ follows a distribution $F$ on $[0,\infty)$. This provides a very flexible family class and by properly choosing the parameters and mixing distribution, many well-known multivariate distributions can be obtained. A prominent example is the generalized hyperbolic (GH) distribution, when the mixing distribution is generalized inverse Gaussian. In this work, we study the tail dependence properties of the GH distribution and derive its coefficient of tail dependence, which describes the joint tail decay rate. Based on this result, a spatio-temporal model for extremes is proposed. The inference of this model can be done via composite likelihood. The model is applied to the wind gust data in the state of Oklahoma, USA and its performance is compared with existing popular models.
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