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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. J. Frank and B. Schweizer, On the duality of generalized infimal and supremal convolutions. Rendiconti di Matematica, 12 (1979), 1–23.
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.
B. Schweizer, Multiplications on the space of probability distribution functions. Aequationes Math. 12 (1975), 156–183.
B. Schweizer and A. Sklar, Probabilistic Metric Spaces. Elsevier North Holland, New York, 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer Basel AG
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive