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2015 | 3 | 1 |
Tytuł artykułu

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

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Abstrakty
EN
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.
Twórcy
autor
  • Deloitte LLP, Audit - Banking & Capital Markets, Hill House, 1 Little New Street, London,
    EC4A 3TR, UK
Bibliografia
  • [1] S. Ahmed, U. Çakmak and A. Shapiro. Coherent risk measures in inventory problems. European J. Oper. Res., 182 (1), 226-238(2007).[WoS]
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  • [4] F. Durante, J. Fernández-Sánchez and C. Sempi. A topological proof of Sklar’s theorem. Appl.Math. Lett. 26, 945-948 (2013).[WoS][Crossref]
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  • [8] E. P. Klement, R. Mesiar and E. Pap. Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms.Fuzzy Set. Syst., 104(1), 3-13 (1999).
  • [9] C. Feng, J. Kowalski, X. M. Tu and H. Wang. A Note on Generalized Inverses of Distribution Function and Quantile Transformation.Applied Mathematics, Scientific Research Publishing, 3 (12A), 2098-2100 (2012).
  • [10] J. F. Mai and M. Scherer. Simulating Copulas. Imperial College Press, London (2012).
  • [11] D. S. Moore and M. C. Spruill. Unified large-sample theory of general Chi-squared statistics for tests of fit. Ann. Statist., 3,599-616 (1975).
  • [12] L. Rüschendorf. On the distributional transform, Sklar’s Theorem, and the empirical copula process. J. Statist. Plann. Inference139(11), 3921-3927 (2009).
  • [13] B. Schweizer and A. Sklar. Operations on distribution functions not derivable from operations on random variables. StudiaMath. 52, 43-52 (1974).
  • [14] B. Schweizer and A. Sklar. Probabilistic metric spaces. North-Holland, New York (1983).
  • [15] A. Sklar. Fonctions de répartition à n dimensions et leursmarges. Publications de l’Institut Statistique de l’Université de Paris8, 229-231 (1959).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_demo-2015-0008
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