Accession Number:

AD0627187

Title:

MONOTONICITY OF RATIOS OF MEANS AND OTHER APPLICATIONS OF MAJORIZATION

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB

Report Date:

1965-12-01

Pagination or Media Count:

25.0

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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE