Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilities of concurrent extremes   The statistical modelling of spatial extremes has recently made major
advances. Much of its focus so far has been on the modelling of the magnitudes
of extreme events but little attention has been paid on the timing of extremes.
To address this gap, this paper introduces the notion of extremal concurrence.
Suppose that one measures precipitation at several synoptic stations over
multiple days. We say that extremes are concurrent if the maximum precipitation
over time at each station is achieved simultaneously, e.g., on a single day.
Under general conditions, we show that the finite sample concurrence
probability converges to an asymptotic quantity, deemed extremal concurrence
probability. Using Palm calculus, we establish general expressions for the
extremal concurrence probability through the max-stable process emerging in the
limit of the componentwise maxima of the sample. Explicit forms of the extremal
concurrence probabilities are obtained for various max-stable models and
several estimators are introduced. In particular, we prove that the pairwise
extremal concurrence probability for max-stable vectors is precisely equal to
the Kendall's $\tau$. The estimators are evaluated by using simulations and
applied to study the concurrence patterns of temperature extremes in the United
States. The results demonstrate that concurrence probability can provide a
powerful new perspective and tools for the analysis of the spatial structure
and impact of extremes.

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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org