MONOTONICITY OF RATIOS OF MEANS AND OTHER APPLICATIONS OF MAJORIZATION

Abstract

Monotonicity of a ratio can be viewed as a form of total positivity. The theory of total positivity is exploited to obtain more general results. The proof of monotonicity is based on a theorem giving sufficient conditions for majorization. Several other applications of the majorization theorem are given. One application concerns a stochastic comparison between a function of order statistics from a distribution with increasing failure rate average and the same function of the order statistics from the exponential distribution. Another application is to a comparison between the condition number of a positive definite matrix and the condition number of a polynomial in the matrix.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1965
Accession Number
AD0627187

Entities

People

  • Albert W. Marshall
  • Frank Proschan
  • Ingram Olkin

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Computing-Related Activities
  • Data Science
  • Distribution Functions
  • Inequalities
  • Information Science
  • Interdisciplinary Science
  • Mathematics
  • Numbers
  • Order Statistics
  • Polynomials
  • Probability
  • Random Variables
  • Real Numbers
  • Real Variables
  • Scientific Research
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.