Towards a simple mathematical theory of citation distributions
نویسنده
چکیده
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.
منابع مشابه
A Simple Transformation Method in Skewness Reduction
Statistical analysis of non-normal data is usually more complicated than that for normaldistribution. In this paper, a simple root/power transformation technique developed by Niaki, et al [1]is extended to transform right and left skewed distributions to nearly normal. The value of theroot/power is explored such that the skewness of the transformed data becomes almost zero with anacceptable err...
متن کاملThermoelastic Analysis of a Functionally Graded Simple Blade Using First-Order Shear Deformation Theory
In this article, the thermo-elastic behavior of a functionally graded simple blade subjected to the mechanical and thermal loadings is presented, applying a semi-analytical method and a variable thickness cantilever beam model. A specific temperature gradient is employed between the root and the edges of the beam. It is assumed that the mechanical and thermal properties are longitudinal directi...
متن کاملComments on Multiparameter Estimation in Truncated Power Series Distributions under the Stein's Loss
This comment is to show that Theorem3.3 of Dey and Chung (1991) (Multiparameter estimation intruncated power series distributions under the Stein's loss.emph{Commun. Statist.-Theory Meth.,} {bf 20}, 309-326) may giveus misleading results. Analytically and through simulation, weshow that the Theorem does not improve the given estimator.
متن کاملItem-time-dependent Lotkaian informetrics and applications to the calculation of the time-dependent h-index and g-index
The model for the cumulative n citation distribution, as developed in [L. Egghe and I.K. Ravichandra Rao. Theory of first-citation distributions and applications. Mathematical and Computer Modelling 34, 81-90, 2001] is extended to the general source-item situation. This yields a time-dependent Lotka function based on a given (static) Lotka function (considered to be valid for time ). Based on t...
متن کاملAdding New Mathematical Functions and Statistical Distributions in WinBUGS
WinBUGS is one of the usual softwares in computational Bayesian statistics, which is used to fit Baysian models easily. Although this software has usual mathematical functions and statistical distributions as built in functions, sometimes it is necessary to include other functions and distributions in computations which is done by some tricks and indirectly. By using WinBUGS developmen...
متن کامل