Inequalities for Propability Contents of Convex Sets via Geometric Average.

Abstract

This paper derives such an inequality for a large class of density functions and a large class fo convex sets. The most general results are given for the bivariate case. An extention to the n-dimensional case appears to be difficult except for some special cases such as the case of independent identically distributed random variables or when the underlying joint density is spherically symmetric. The class of convex sets considered includes D sub infinity and D sub 2 as special cases and special applications are given for elliptically contoured distributions and scale parameters families. In all these cases, universal upper bounds on the probability contents can be given by substituting the values of the a sub i's by their geometric mean.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA169938

Entities

People

  • Moshe Shaked
  • Y. L. Tong

Organizations

  • University of Arizona

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Bodies
  • Convex Bodies
  • Convex Sets
  • Ellipsoids
  • Inequalities
  • Normal Distribution
  • Permutations
  • Probability
  • Procurement
  • Random Variables
  • Symmetry
  • Theorems
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.