Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Squaring the Circle and Cubing the Sphere: Circular and Spherical
  Copulas   Do there exist circular and spherical copulas in $R^d$? That is, do there
exist circularly symmetric distributions on the unit disk in $R^2$ and
spherically symmetric distributions on the unit ball in $R^d$, $d\ge3$, whose
one-dimensional marginal distributions are uniform? The answer is yes for $d=2$
and 3, where the circular and spherical copulas are unique and can be
determined explicitly, but no for $d\ge4$. A one-parameter family of elliptical
bivariate copulas is obtained from the unique circular copula in $R^2$ by
oblique coordinate transformations. Copulas obtained by a non-linear
transformation of a uniform distribution on the unit ball in $R^d$ are also
described, and determined explicitly for $d=2$.

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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci