Power Laws in the Information Production Process: Lotkaian Informetrics (Hardcover)
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This book describes informetric results from the point of view of Lotkaian size-frequency functions, i.e. functions that are decreasing power laws. Explanations and examples of this model are given showing that it is the most important regularity amongst other possible models. This theory is then developed in the framework of IPPs (Information Production Processes) hereby also indicating its relation with e.g. the law of Zipf.
Applications are given in the following fields: three-dimensional informetrics (positive reinforcement and Type/Token-Taken informetrics), concentration theory (including the description of Lorenz curves and concentration measures in Lotkaian informetrics), fractal complexity theory (Lotkaian informetrics as self-similar fractals), Lotkaian informetrics in which items can have multiple sources (where fractional size-frequency functions are constructed), the theory of first-citation distributions and the N-fold Cartesian product of IPPs (describing frequency functions for N-grams and N-word phrases). In the Appendix, methods are given to determine the parameters in the law of Lotka, based on a set of discrete data.
The book explains numerous informetric regularities, only based on a decreasing power law as size-frequency function, i.e. Lotka's law. It revives the historical formulation of Alfred Lotka of 1926 and shows the power of this power law, both in classical aspects of informetrics (libraries, bibliographies) as well as in "new" applications such as social networks (citation or collaboration networks and the Internet).
Table of Contents:
Introduction. Chapter I. Lotkaian Informetrics: An Introduction. Informetrics. What is Lotkaian informetrics? Why Lotkaian informetrics? Practical Examples of Lotkaian Informetrics. Chapetr II. Basic Theory of Lotkaian Informetrics. General Informetrics Theory. Theory of Lotkaian Informetrics. Extension of the General Informetrics Theory: The Dual Size-Frequency Function H. The Place of the Law of Zipf in Lotkaian Informetrics. Chapter III. Three-dimensional Lotkaian Informetrics. Linear Three-Dimensional Lotkaian Informetrics. Chapter IV. Lotkaian Concentration Theory. Introduction. Discrete Concentration Theory. Continuous Concentration Theory. Concentration Theory of Linear Three-Dimensional Informetrics. Chapter V. Lotkaian Fractal Complexity Theory. Introduction. Elements of Fractal Theory. Interpretation of Lotkaian IPPs as Self-Similar Fractals. Chapter VI. Lotkaian Informetrics of Systems in which Items can have Multiple Sources. Introduction. Crediting Systems and Counting Procedures for Sources and "Super Sources" in IPPs Where Items Can Have Multiple Sources. Construction of Fractional Size-Frequency Functions Based on Two Dual Lotka laws. Chapter VII. Further Applications in Lotkaian Informetrics. Introduction. Explaining "Regularities". Probabilistic Explanation of the Relationship Between Citation Age and Journal Productivity. Chapter VII. General and Lotkaian Theory of the Distribution of Author Ranks in Multi-Authored Papers. The First-Citation Distribution in Lotkaian Informetrics. Zipfian Theory of N-grams and of N-word Phrases: the Cartesian Product of IPPs. Appendix. Appendix I. Appendix II. Appendix III Statistical Determination of the Parameters in the Law of Lotka. Bibliography. Subject Index.