Some recent developments on majorization inequalities in probability and statistics
The author reviews some recent developments on majorization inequalities in probability and statistics. He describes some related generalizations, including majorization in an integral form, multivariate majorization, stochastic majorization, and other related orderings (including the Lorenz ordering and the arrangement increasing ordering) and he states some results. He discusses partial orderings of probability contents of certain classes of geometric regions in \({\mathbb{R}}^ n\) via a majorization ordering of their parameter vectors, and he deals with some applications of majorization theory to dependence and peakedness orderings of random variables. In most cases the described results became available since the publication of the book by \textit{A. W. Marshall} and \textit{I. Olkin} [Inequalities: Theory of majorization and its applications (1979; Zbl 0437.26007)].
scientific article; zbMATH DE number 566091
scientific article