A Simple Integral Representation for the Second Moments of Additive Random Variables on Stochastic Polyhedra

  • Let \(a_1, i:=1,\dots,m\), be an i.i.d. sequence taking values in \(\mathbb{R}^n\), whose convex hull is interpreted as a stochastic polyhedron \(P\). For a special class of random variables, which decompose additively relative to their boundary simplices, eg. the volume of \(P\), simple integral representations of its first two moments are given in case of rotationally symmetric distributions in order to facilitate estimations of variances or to quantify large deviations from the mean.
Author:Karl-Heinz Küfer
Series (Serial Number):Preprints (rote Reihe) des Fachbereich Mathematik (223)
Document Type:Report
Language of publication:English
Date of Publication (online):2017/11/07
Year of first Publication:1992
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/07
Page Number:16
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)