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MONOTONICITY OF RATIOS OF MEANS AND OTHER APPLICATIONS OF MAJORIZATION

Albert W. Marshall, Ingram Olkin, Frank Proschan

Abstract

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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Available abstract

Key concepts: Majorization, Monotonic function, Mathematics, Statistics, Econometrics, Computer science, Combinatorics, Mathematical analysis