Webmajorization and/or Lorenz ordering played an, often important, role in the analysis. Over the years, the number of such examples has naturally increased. There were ten examples of such applications in the final chapter of the first edition. There are now 24, spread over two chapters. These examples reinforce the belief that majorization WebAs observed in Avérous et al. and Genest et al. , there is a close connection between the above concepts of more dependence and the notion of dispersive ordering. 2.5. Notions of Majorization and Related Orderings. One of the basic tools in establishing various inequalities in statistics and probability is the notion of majorization.

(PDF) Completely Monotone Functions: A Digest (2014) Milan …

WebThe majorization partial order on finite sets, described here, can be generalized to the Lorenz ordering, a partial order on distribution functions. For example, a wealth distributionis Lorenz-greater than another iff its Lorenz curvelies belowthe other. Web18 feb. 2024 · Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the … get red sauce stain out of shirt

Majorization, Randomness and Dependence for Multivariate Distributions

Webthe majorization pre-ordering ≺ on An (that is, the function ϕis Schur-convex on An) if and only if it is symmetric and the function ψ(x1) in Corollary 1 is non-decreasing in t/2 ≤ x1 ≤ t. Corollary 2 Let ϕ: An → R be a symmetric function that … WebAn important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local operations and classical communication) ? Mathematically, the question amounts to describe, for a fixed … Weberal majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and flex-ible surrogates via convex functions. Classical orthogonality, aber-ration and uniformity criteria are unified by choosing combinatorial and exponential kernels. A construction method is also sketched out. 1. get red stain out of white shirt