Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-exchangeability of copulas arising from shock models   When choosing the right copula for our data a key point is to distinguish the
family that describes it at the best. In this respect, a better choice of the
copulas could be obtained through the information about the (non)symmetry of
the data. Exchangeability as a probability concept (first next to independence)
has been studied since 1930's, copulas have been studied since 1950's, and even
the most important class of copulas from the point of view of applications,
i.e. the ones arising from shock models s.a. Marshall's copulas, have been
studied since 1960's. However, the point of non-exchangeability of copulas was
brought up only in 2006 and has been intensively studied ever since. One of the
main contributions of this paper is the maximal asymmetry function for a family
of copulas. We compute this function for the major families of shock-based
copulas, i.e. Marshall, maxmin and reflected maxmin (RMM for short) copulas and
also for some other important families. We compute the sharp bound of asymmetry
measure $\mu_\infty$, the most important of the asymmetry measures, for the
family of Marshall copulas and the family of maxmin copulas, which both equal
to $\frac{4}{27}\ (\approx 0.148)$. One should compare this bound to the one
for the class of PQD copulas to which they belong, which is $3-2\sqrt{2}\
\approx 0.172)$, and to the general bound for all copulas that is $\frac13$.
Furthermore, we give the sharp bound of the same asymmetry measure for RMM
copulas which is $3-2\sqrt{2}$, compared to the same bound for NQD copulas,
where they belong, which is $\sqrt{5}-2\ (\approx 0.236)$. One of our main
results is also the statistical interpretation of shocks in a given model at
which the maximal asymmetry measure bound is attained. These interpretations
for the three families studied are illustrated by examples that should be
helpful to practitioners when choosing the model for their data.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs