We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy”. Upper and lower error bars on the accuracy are provided by the...

To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Cl...

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented.

Abstract It is well-known that using arithmetic averages of yearly return observations leads to downward biased discount rates estimations. Well-known corrections, however, lead upward results under the presence negative serial correlation. Using a simulation analysis, we first show specific variant Cooper estimator, labelled as C4 in this paper, robust estimations even both correlation and het...

Comparative evaluations of information retrieval systems are based on a number of key premises, including that representative topic sets can be created, that suitable relevance judgements can be generated, and that systems can be sensibly compared based on their aggregate performance over the selected topic set. This paper considers the role of the third of these assumptions – that the performa...

In a recent pilot study, errors in forecasts of future returns showed little differences when arithmetic and geometric mean calculations served as the basis for the projections. Using annual returns on the DJIA and S&P for 1954 to 2007, 1-year-, 5-year-ahead, and 10-year-ahead forecasts were made based on 5-, 10-, 15-, and 20-year histories based on both arithmetic and geometric averages. This ...

Peripheral nerve cross sections were analyzed for the variation in peripheral nerve histograms obtained along a single short segment of cat saphcnous nerve. Individual myelinatcd fibers in one fasciclc were traced through nine sequential sections. Two mean fiber diameter histograms were obtained from the sequential cross sections : a “mean fiber diameter histogram” constructed from the arithmet...