Two Basic Partial Orderings for Distributions Derived from Schur Functions and Majorization

Abstract

Researchers in applied fields have long recognized the usefulness of inequalities when exact results are not available. The use of inequalieis allows us to say that one estimate is better than another, that one maintenance policy is better than another or that a certain selection procedure is better than another or that a certain selection procedure is better than another etc., even though, we may not know the best estimator, the best maintenance policy or the best selection procedure. Such results are generally obtained from inequalities between two probability measures or random variables. Inequalities between random variables are in turn obtained from deterministic inequalities or deterministic partial orderings. In this expository paper, the authors describe the essentials of stochastic majorization and DT ordering and demonstrate some applications. A nenw proof of a slight generalization of earlier result on DT ordering and demonstrate some applications. A new proof of a slight generalization of earlier result on DT functions is given. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1989
Accession Number
ADA213703

Entities

People

  • Jayaram Sethuraman
  • Kumar Joag-dev

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Books
  • Convex Sets
  • Estimators
  • Families (Human)
  • Inequalities
  • Maintenance
  • Military Research
  • Permutations
  • Poisson Density Functions
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistics
  • Theorems
  • United States
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Instructional Design and Training Evaluation.
  • Mathematical Modeling and Probability Theory.