Statistical methods in information science, Gini coefficient, Lorenz curve, Diversity index (Statistics), and Mathematics

Balance (or evenness) as used in conventional approaches to measuring diversity needs careful definition. Nijssen et al. (Coenoses 13(1):33–38, 1998) used a mathematical approach to show that the Lorenz curve is an adequate representation of evenness and proposed that the Gini coefficient is a perfect indicator of balance. In this paper, we take an alternative thermodynamic perspective that leads to a very simple dimensionless measure of balance that ranges from 0 (perfect balance or evenness) to 1 (perfect unevenness or absolute concentration). It has the expected permutation invariance, scaling invariance, and replication invariance properties of a good evenness indicator and also has sensitivity to the transfer requirements (i.e. sensing the entropy changes correctly). It also has a naturalness property. [ABSTRACT FROM AUTHOR]

Databases, Electronic information resources, Bibliographic databases, Statistical methods in information science, Bibliometrics, Mathematics, and Scientometrics

We analyze the data about works (papers, books) from the time period 1990-2010 that are collected in Zentralblatt MATH database. The data were converted into four 2-mode networks (works $$\times $$ authors, works $$\times $$ journals, works $$\times $$ keywords and works $$\times $$ mathematical subject classifications) and into a partition of works by publication year. The networks were analyzed using Pajek-a program for analysis and visualization of large networks. We explore the distributions of some properties of works and the collaborations among mathematicians. We also take a closer look at the characteristics of the field of graph theory as were realized with the publications. [ABSTRACT FROM AUTHOR]

Statistical methods in information science, Weibull distribution, Power law (Mathematics), Pareto analysis, and Mathematics

Based on three theorems for size-to-rank transformations, the shifted power function is used to set up a theoretical framework unifying informetric distributions. While the shifted power function with time-type exponential cutoff supplies a unifying informetric framework, the shifted power function with space-type exponential cutoff can be linked to the Pareto and Weibull distributions. The exponent is the crucial parameter in a power function, determining the most important characteristics of the power-law distribution. [ABSTRACT FROM AUTHOR]