Averages of ratios compared to ratios of averages: Mathematical results
نویسندگان
چکیده
منابع مشابه
Averages of ratios vs. ratios of averages: An empirical analysis of four levels of aggregation
In the recent debate on the use of averages of ratios (AoR) and ratios of averages (RoA) for the compilation of field-normalized citation rates, little evidence has been provided on the different results obtained by the two methods at various levels of aggregation. This paper provides such an empirical analysis at the level of individual researchers, departments, institutions and countries. Two...
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It follows from Birkhoff’s Ergodic Theorem that the irregular set of points for which the Birkhoff averages of a given continuous function diverge has zero measure with respect to any finite invariant measure. In strong contrast, for systems with the weak specification property, we show here that if the irregular set is nonempty, then it is residual. This includes topologically transitive topol...
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We study the averages of ratios of characteristic polynomials over circular β-ensembles, where β is a positive real number. Using Jack polynomial theory, we obtain three expressions for ratio averages. Two of them are given as sums of super-Jack polynomials and another one is given by a hyperdeterminant. As applications, we give dualities for ratio averages between β and 4/β. MSC-class: primary...
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Averages of ratios of characteristic polynomials for the compact classical groups are evaluated in terms of determinants whose dimensions are independent of the matrix rank. These formulas are shown to be equivalent to expressions for the same averages obtained in a previous study, which was motivated by applications to analytic number theory. Our approach uses classical methods of random matri...
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ژورنال
عنوان ژورنال: Journal of Informetrics
سال: 2012
ISSN: 1751-1577
DOI: 10.1016/j.joi.2011.12.007