Empirical hyperbolic distributions (Bradford-Zipf-Mandelbrot) for bibliometric description and prediction

Purpose – Aims to build on the work of Buckland and Hindle regarding statistical distribution as applied to the field of bibliometrics, particularly the use of empirical laws. Design/methodology/approach – Gives examples of hyperbolic distributions that have a bearing on the bibliometric application, and discusses the characteristics of hyperbolic distributions and the Bradford distribution. Findings – Hyperbolic distributions are the inevitable result of combinatorial necessity and a tendency to short-term rational behaviour. Originality/value – Supports Bradford’s conclusion from his law, i.e. that to know about one’s speciality, one must go outside it.

[1]  WILLIAM GOFFMAN,et al.  Mathematical Approach to the Spread of Scientific Ideas—the History of Mast Cell Research , 1966, Nature.

[2]  WILLIAM GOFFMAN,et al.  Stability of Epidemic Processes , 1966, Nature.

[3]  George Kingsley Zipf,et al.  The Psychobiology of Language , 2022 .

[4]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[5]  Benoit B. Mandelbrot,et al.  Self-Similar Error Clusters in Communication Systems and the Concept of Conditional Stationarity , 1965 .

[6]  Alfred J. Lotka,et al.  The frequency distribution of scientific productivity , 1926 .

[7]  S. Bradford "Sources of information on specific subjects" by S.C. Bradford , 1985 .

[8]  John D. Leith Biomedical literature: analysis of journal articles collected by a radiation- and cell-biologist , 1969 .

[9]  P. Zunde,et al.  Distribution of indexing terms for maximum efficiency of information transmission , 1967 .

[10]  WILLIAM GOFFMAN,et al.  Generalization of Epidemic Theory: An Application to the Transmission of Ideas , 1964, Nature.

[11]  Ferdinand F. Leimkuhler,et al.  THE BRADFORD DISTRIBUTION , 1967 .

[12]  Gustav Herdan,et al.  The advanced theory of language as choice and chance , 1968 .

[13]  Jay M. Berger,et al.  A New Model for Error Clustering in Telephone Circuits , 1963, IBM J. Res. Dev..

[14]  M. G. Kendall,et al.  The Bibliography of Operational Research , 1960 .

[15]  W. Bateson,et al.  Age and Area: A Study in Geographical Distribution and Origin of Species , 1923, Nature.

[16]  WILLIAM GOFFMAN An Epidemic Process in an Open Population , 1965, Nature.

[17]  B. Mandelbrot How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[18]  R. A. Fairthorne,et al.  Towards information retrieval , 1961 .

[19]  G. Yule,et al.  A Mathematical Theory of Evolution Based on the Conclusions of Dr. J. C. Willis, F.R.S. , 1925 .

[20]  A. D. Booth,et al.  ON THE GEOMETRY OF LIBRARIES , 1969 .

[21]  B. C. Brookes THE DERIVATION AND APPLICATION OF THE BRADFORD‐ZIPF DISTRIBUTION , 1968 .

[22]  W. Goffman,et al.  Communication and epidemic processes , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  Kenneth C. Lynn,et al.  A quantitative comparison of conventional information compression techniques in dental literature , 1969 .

[24]  Ole V. Groos Bradford's law and the keenan-atherton data , 1967 .

[25]  B.Sc. R.A. Fairthorne,et al.  AUTOMATA AND INFORMATION , 1952 .

[26]  W. Goffman,et al.  Dispersion of Papers among Journals based on a Mathematical Analysis of Two Diverse Medical Literatures , 1969, Nature.

[27]  A. F. Parker-Rhodes,et al.  A Theory of Word-Frequency Distribution , 1956, Nature.

[28]  W. H. Furry,et al.  Distribution of Numbers and Distribution of Significant Figures , 1945, Nature.

[29]  P. Zunde,et al.  Indexing Consistency and Quality. , 1969 .

[30]  B. Mandelbrot The Variation of Certain Speculative Prices , 1963 .

[31]  Eugene Wall,et al.  The distribution of term usage in manipulative indexes , 1964 .

[32]  Brian Vickery,et al.  BRADFORD'S LAW OF SCATTERING , 1948 .

[33]  E. Fama Mandelbrot and the Stable Paretian Hypothesis , 1963 .

[34]  P. F. Cole A NEW LOOK AT REFERENCE SCATTERING , 1962 .

[35]  B.Sc. R.A. Fairthorne INFORMATION THEORY AND CLERICAL SYSTEMS , 1953 .

[36]  S. A. GOUDSMIT,et al.  Significant Figures of Numbers in Statistical Tables , 1944, Nature.