66 research outputs found
Joint Mixability of Elliptical Distributions and Related Families
In this paper, we further develop the theory of complete mixability and joint
mixability for some distribution families. We generalize a result of
R\"uschendorf and Uckelmann (2002) related to complete mixability of continuous
distribution function having a symmetric and unimodal density. Two different
proofs to a result of Wang and Wang (2016) which related to the joint
mixability of elliptical distributions with the same characteristic generator
are present. We solve the Open Problem 7 in Wang (2015) by constructing a
bimodal-symmetric distribution. The joint mixability of slash-elliptical
distributions and skew-elliptical distributions is studied and the extension to
multivariate distributions is also investigated.Comment: 15page
Sharp convex bounds on the aggregate sums--An alternative proof
It is well known that a random vector with given marginal distributions is
comonotonic if and only if it has the largest sum with respect to the convex
order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric
proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32,
71-80. Cheung (2010), Characterizing a comonotonic random vector by the
distribution of the sum of its components, Insurance: Mathematics and Economics
47(2), 130-136] and that a random vector with given marginal distributions is
mutually exclusive if and only if it has the minimal convex sum [Cheung and Lo
(2014), Characterizing mutual exclusivity as the strongest negative
multivariate dependence structure, Insurance: Mathematics and Economics 55,
180-190]. In this note, we give a new proof of this two results using the
theories of distortion risk measure and expected utility.Comment: 11page
Hessian and increasing-Hessian orderings of multivariate skew-elliptical random vectors
In this work, we establish some stochastic comparison results for
multivariate skew-elliptical random vectors. These multivariate stochastic
comparisons involve Hessian and increasing-Hessian orderings as well as many of
their special cases. Necessary and/or sufficient conditions of the orderings
are provided simply based on a comparison of the underlying model parameters.Comment: 2
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