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]
Malaysian Journal of Library & Information Science. 2014, Vol. 19 Issue 1, p1-15. 15p.
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]
Zou, Yuan, Mathematics & Statistics, Faculty of Science, UNSW
Image processing, Filters, Mathematics, Statistical methods, and Thesis digitisation program
In the last few decades, a number of nonlinear filters were presented, especially in the electrical engineering literature. One of the most popular nonlinear filters is weighted median filtering. The main objective of this thesis is to analyse the statistical and deterministic properties of the weighted median filter and some related nonlinear filters with applications in image processing. The output distribution of the weighted median filter with independent but not identically distributed inputs is derived. The joint distributions of the outputs of the median and weighted median filters with independent but not identically distributed inputs on overlapping windows are obtained. As an application, these results are used to compute the power function for detecting a step change in images by using a range of existing window shapes for the median filter and weighting schemes for the weighted median filter. As an extension of max/median filtering, generalized max/median filtering is proposed. The relationship between them is given. The output distributions of generalized max/median filtering and some other modified median filtering are derived. Using these results, statistical evaluations are obtained to show how well these filters can suppress noise and preserve image details. Simulation results for these modified median filters are presented. Stack filtering is briefly reviewed. Some new expressions of the output distribution and joint distribution for stack filtering are derived. Applications of stack filtering are illustrated by examples. Statistical comparisons between the weighted median and modified median filters are presented. Exponential weighted median filters, a general parametric class of the weighted median filter, are evaluated for their ability to approximate the behaviour of the other filters considered. Statistical analyses are given to compare some well known weighted median filters. The final chapter reviews some methods for edge detection. A generalized real root signal and a generalized root signal of two dimensional median filtering are defined. A new edge detection method based on them is proposed and compared with conventional edge detectors.
PRODUKTIONSPLÄNE + ABLAUFPLANUNG (PRODUKTION); STATISTISCHE METHODEN IN TECHNIK, PRODUKTION UND OPERATIONS RESEARCH (MATHEMATISCHE STATISTIK); PRODUCTION SCHEDULING + PROCESS ROUTING (PRODUCTION); STATISTICAL METHODS IN TECHNOLOGY, MANUFACTURING AND OPERATIONS RESEARCH (MATHEMATICAL STATISTICS), Mathematics, and Economics