Generalized increasing convex and directionally convex orders

In this paper, the componentwise increasing convex order, the upper orthant order, the upper orthant convex order and the increasing directionally convex order for random vectors are generalized to hierarchical classes of integral stochastic order relations. The elements of the generating classes of functions possess non-negative partial derivatives up to some given degrees. Some properties of these new stochastic order relations are studied. A particular attention is paid to the comparison of weighted sums of the respective components of ordered random vectors. By providing a unified derivation of standard multivariate stochastic orderings, the present paper shows how some well-known results derive from a common principle.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2010
Language	Anglais
Number of pages	13 pages
Collection	ISBA Discussion Paper - 1012
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	integral stochastic orders ; supermodular functions ; directionally convex functions
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html http://hdl.handle.net/2078.1/115179[Handle]

See also
	[boreal:33968]	Generalized Increasing Convex and Directionally Convex Orders