An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

Frank Oertel

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 113-125, electronic only
  • ISSN: 2300-2298

Abstract

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We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.

How to cite

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Frank Oertel. "An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem." Dependence Modeling 3.1 (2015): 113-125, electronic only. <http://eudml.org/doc/275903>.

@article{FrankOertel2015,
abstract = {We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.},
author = {Frank Oertel},
journal = {Dependence Modeling},
keywords = {Copulas, distributional transform; generalised inverse functions; Sklar’s Theorem; copulas; distributional transform; Sklar's theorem},
language = {eng},
number = {1},
pages = {113-125, electronic only},
title = {An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem},
url = {http://eudml.org/doc/275903},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Frank Oertel
TI - An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 113
EP - 125, electronic only
AB - We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.
LA - eng
KW - Copulas, distributional transform; generalised inverse functions; Sklar’s Theorem; copulas; distributional transform; Sklar's theorem
UR - http://eudml.org/doc/275903
ER -

References

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  12. [12] L. Rüschendorf. On the distributional transform, Sklar’s Theorem, and the empirical copula process. J. Statist. Plann. Inference 139(11), 3921-3927 (2009). Zbl1171.60313
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