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Functions operating on several multivariate distribution functions

Author

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  • Ressel Paul

    (MGF, Kath. Universität Eichstätt-Ingolstadt, Ostenstr. 26, Eichstätt, Germany)

Abstract

Functions f f on [ 0 , 1 ] m {\left[0,1]}^{m} such that every composition f ∘ ( g 1 , … , g m ) f\circ \left({g}_{1},\ldots ,{g}_{m}) with d d -dimensional distribution functions g 1 , … , g m {g}_{1},\ldots ,{g}_{m} is again a distribution function, turn out to be characterized by a very natural monotonicity condition, which for d = 2 d=2 means ultramodularity. For m = 1 m=1 (and d = 2 d=2 ), this is equivalent with increasing convexity.

Suggested Citation

  • Ressel Paul, 2023. "Functions operating on several multivariate distribution functions," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-11, January.
    • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:11:n:1
    DOI: 10.1515/demo-2023-0104
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    References listed on IDEAS

    as
    1. Massimo Marinacci & Luigi Montrucchio, 2005. "Ultramodular Functions," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 311-332, May.
    2. Ressel, Paul, 2012. "Functions operating on multivariate distribution and survival functions—With applications to classical mean-values and to copulas," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 55-67.
    3. Ressel, Paul, 2011. "Monotonicity properties of multivariate distribution and survival functions -- With an application to Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 393-404, March.
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