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A Functional Inequality for Distribution Functions

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General Inequalities 3

Abstract

In this paper, we study the functional inequality τ(F ∘ H,G ∘ K) ≥ τ(F,G) ∘ τ(H,K), where F, G, H, and K are arbitrary distribution functions in Δ+, ∘ denotes composition, and the unknown τ; is a certain binary operation on the set Δ+ of positive distribution functions.

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References

  1. M. J. Frank and B. Schweizer, On the duality of generalized infimal and supremal convolutions. Rendiconti di Matematica, 12 (1979), 1–23.

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  2. R. Moynihan, B. Schweizer, and A. Sklar, Inequalities among operations on probability distribution functions, pp. 133–149 in: General Inequalities 1, ed. E. F. Beckenbach. Birkhaüser Verlag, Basel, 1978.

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  3. B. Schweizer, Multiplications on the space of probability distribution functions. Aequationes Math. 12 (1975), 156–183.

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  4. B. Schweizer and A. Sklar, Probabilistic Metric Spaces. Elsevier North Holland, New York, 1982.

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© 1983 Springer Basel AG

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Alsina, C. (1983). A Functional Inequality for Distribution Functions. In: Beckenbach, E.F., Walter, W. (eds) General Inequalities 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 64. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6290-5_18

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  • DOI: https://doi.org/10.1007/978-3-0348-6290-5_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6292-9

  • Online ISBN: 978-3-0348-6290-5

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