Bradford's distribution: From the classical bibliometric "law" to the more general stochastic models

Journal of the American Society for Information Science

Volumn 48, Issue 9, 1997, Pages 833-842

  Oluić Vuković, Vesna ^a  

^a ProRes Ltd   (Croatia)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STRUCTURES; DATABASE SYSTEMS; INFORMATION DISSEMINATION; RANDOM PROCESSES;

BRADFORD'S DISTRIBUTION;

BIBLIOGRAPHIC RETRIEVAL SYSTEMS;

EID: 0031238330     PISSN: 00028231     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-4571(199709)48:9<833::AID-ASI7>3.0.CO;2-S     Document Type: Article

References (130)

1. Ajiferuke, I. (1991). A probabilistic model for the distribution of authorships. Journal of the American Society for Information Science, 42, 279-289.
2. Ajiferuke, I., & Tague, J. M. (1990). A model for the full circulation data. In L. Egghe & R. Rousseau (Eds.), Informetrics 89/90: Select proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics (pp. 1-16). Amsterdam: Elsevier.
3. Asai, I. (1981). A general formulation of Bradford's distribution: The graph-oriented approach. Journal of the American Society for Information Science, 32, 113-119.
4. Basu, A. (1992). Hierarchical distributions and Bradford's law. Journal of the American Society for Information Science, 43, 494-500.
5. Bookstein, A. (1979). Explanations of the bibliometric laws. Collection Management, 3, 151-162.
6. Bookstein, A. (1990a). Informetric distributions, part I: Unified overview. Journal of the American Society for Information Science, 41, 368-375.
7. Bookstein, A. (1990b). Informetric distributions, part II: Resilience to ambiguity. Journal of the American Society for Information Science, 41, 376-386.
8. Bradford, S. C. (1934). Sources of information on specific subjects. Engineering, 137, 85-86.
9. Braga, G. M. (1978). Some aspects of Bradford's distribution. Proceedings of the ASIS Annual Meeting, 15, 51-54.
10. Brookes, B. C. (1968). The derivation and application of the Bradford-Zipf distribution. Journal of Documentation, 24, 247-265.
11. Brookes, B. C. (1969). Bradford's law and the bibliography of science. Nature, 224, 953-956.
12. Brookes, B. C. (1977). Theory of the Bradford law. Journal of documentation, 33, 180-209.
13. Brookes, B. C. (1981). A critical commentary on Leimkuhler's "exact" formulation of the Bradford law. Journal of Documentation, 37, 77-88.
14. Brookes, B. C. (1982). Quantitative analysis in the humanities: The advantage of ranking techniques. In H. Guiter & M. V. Arapov (Eds.), Studies on Zipf's Law (pp. 65-115). Bochum, Germany: Brockmeyer.
15. Brookes, B. C. (1984). Towards informetrics: Haitun, Laplace, Zipf, Bradford and the Alvey programme. Journal of Documentation, 40, 120-143.
16. Brookes, B. C. (1988). Comments on the scope of bibliometrics. In L. Egghe & R. Rousseau (Eds.), Informetrics 87/88: Select proceedings of the First International Conference on Bibliometrics and Theoretical Aspects of Information Retrieval (pp. 29-41). Amsterdam: Elsevier.
17. Brookes, B. C., & Griffiths, J. M. (1978). Frequency-Rank distributions. Journal of the American Society for Information Science, 29, 5-13.
18. Brooks, T. A. (1990). Literature core zones adjusted by impact factor. Journal of Information Science, 16, 51-57.
19. Burrell, Q. L. (1980). A simple stochastic model for library loans. Journal of Documentation, 36, 115-132.
20. Burrell, Q. L. (1982). Alternative models for library circulation data. Journal of Documentation, 38, 1-13.
21. Burrell, Q. L. (1985). The 80/20 rule: Library lore or statistical law? Journal of Documentation, 41, 24-39.
22. Burrell, Q. L. (1987). A third note on ageing in library circulation model: Applications to future use and relegation. Journal of Documentation, 43, 24-45.
23. Burrell, Q. L. (1988a). Modelling the Bradford phenomenon. Journal of Documentation, 44, 1-18.
24. Burrell, Q. L. (1988b). Predictive aspects of some bibliometric processes. In L. Egghe & R. Rousseau (Eds.), Informetrics 87/88: Select proceedings of the First International Conference on Bibliometrics and Theoretical Aspects of Information Retrieval (pp. 43-63). Amsterdam: Elsevier.
25. Burrell, Q. L. (1990). Using the gamma-Poison model to predict library circulations. Journal of the American Society for Information Science, 41, 164-170.
26. Burrell, Q. L. (1991a). The Bradford distribution and the Gini index. Scientometrics, 21, 117-130.
27. Burrell, Q. L. (1991b). The dynamic nature of bibliometric processes: A case study. Third International Conference on Informetrics, Bangalore, India: Indian Statistical Institute.
28. Burrell, Q. L. (1992). The Gini index and the Leimkuhler curve for bibliometric processes. Information Processing & Management, 28, 19-33.
29. Burrell, Q. L. (1993). Yes, the GIGP really does work - and is workable! Journal of the American Society for Information Science, 44, 61-69.
30. Burrell, Q. L. (1994). Scientstochastic? Scientometrics, 30, 505-509.
31. Burrell, Q. L., & Cane, V. R. (1982). The analysis of library data (with discussion). Journal of the Royal Statistical Society, Series A, 145, 439-471.
32. Cane, V. R. (1977). A class of non-identifiable stochastic models. Journal of Applied Probability, 14, 475-482.
33. Champemowne, D. G. (1953). A model of income distribution. Economical Journal, 63, 318-315.
34. Chen, Y. S. (1989). Analysis of Lotka's law: The Simon-Yule approach. Information Processing and Management, 25, 527-544.
35. Chen, Y. S., Chong, P. P., & Kim, J. S. (1992). Self-adaptive statistical language model for speech recognition. Cybernetica, 35, 103-127.
36. Chen, Y. S., Chong, P. P., & Tong, Y. (1993). Theoretical foundation of the 80/20 rule. Scientometrics, 28, 183-204.
37. Chen, Y. S., Chong, P. P., & Tong, Y. (1994). The Simon-Yule approach to bibliometric modeling. Information Processing & Management, 30, 535-556.
38. Chen, Y. S., Chong, P. P., & Tong, Y. (1995). Dynamic behavior of Bradford's Law. Journal of the American Society for Information Science, 46, 370-383.
39. Chen, Y. S., & Leimkuhler, F. F. (1986). A relationship between Lotka's law, Bradford's law, and Zipf's law. Journal of the American Society for Information Science, 37, 307-314.
40. Chen, Y. S., & Leimkuhler, F. F. (1989). A type-token identity in the Simon-Yule model of text. Journal of the American Society for Information Science, 40, 45-53.
41. Cocks, T. M., & Brookes, B. C. (1986). Sichel's unification of bibliometric frequency distributions. Journal of Information Science, 12, 45-51.
42. Egghe, L. (1985). Consequences of Lotka's law for the law of Bradford. Journal of Documentation, 41, 173-189.
43. Egghe, L. (1988). On the classification of the classical bibliometric laws. Journal of Documentation, 44, 53-62.
44. Egghe, L. (1990a). Applications of the theory of Bradford's law to the calculation of Leimkuhler's law and to the completion of bibliographies. Journal of the American Society for Information Science, 41, 469-492.
45. Egghe, L. (1990b). The duality of informetric systems with applications to the empirical laws. Journal of Information Science, 16, 17-27.
46. Egghe, L. (1990c). New Bradfordian laws equivalent with old Lotka laws, evolving from a source-item duality argument. In L. Egghe & R. Rousseau (Eds.), Informetrics 89/90: Select proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics (pp. 97-137). Amsterdam: Elsevier.
47. Egghe, L., & Rousseau, R. (1988). Reflections on a deflection: A note on different causes of the Groos droop. Scientometrics, 14, 493-511.
48. Egghe, L., & Rousseau, R. (1990). Introduction to informetrics: Quantitative methods in library, documentation and information science. Amsterdam: Elsevier.
49. Egghe, L., & Rousseau, R. (1995). Generalized success-breeds-success principle leading to time-dependent informetric distributions. Journal of the American Society for Information Science, 46, 426-445.
50. Egghe, L., & Rousseau, R. (1996). Stochastic processes determined by a general success-breeds-success principle. Mathematical and Computer Modelling, 23, 93-104.
51. Fairthorne, R. A. (1969). Empirical hyperbolic distributions (Bradford-Zipf-Mandelbrot) for bibliometric description and prediction. Journal of Documentation, 25, 319-343.
52. Fedorowicz, J. (1982). The theoretical foundation of Zipf's law and its application to the bibliographic database environment. Journal of the American Society for Information Science, 33, 285-293.
53. Feller, W. (1943). On a general class of "contagious" distribution. Annals of Mathematical Statistics, 14, 389-400.
54. Glanzel, W., & Schubert, A. (1990). The cumulative advantage function. A mathematical formulation based on conditional expectations and its application to scientometric distribution. In L. Egghe & R. Rousseau (Eds.), Informetrics 89/90: Select proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics (pp. 139-147). Amsterdam: Elsevier.
55. Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-264.
56. Greenwood, M., & Yule, G. U. (1920). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference of the occurrence of multiple attacks of disease or of repeated accidents. Journal of the Royal Statistical Society, 83, 255-279.
57. Groos, O. V. (1967). Bradford's law and the Keenan-Atherton data. American Documentation, 18, 46.
58. Haight, A. F., & Jones, B. R. (1974). A probabilistic treatment of qualitative data with special reference to word association tests. Journal of Mathematical Psychology, 11, 237-244.
59. Haitun, S. D. (1982). Stationary informetric distributions: Part I, different approximations; Part II, non-Gaussian nature of scientific activities; Part III, the role of the Zipf distribution. Scientometrics, 4, 5-25, 89-104, 181-194.
60. Haspers, J. H. (1976). The yield formula and Bradford's law. Journal of the American Society for Information Science, 27, 281-287.
61. Herdan, G. (1961). A critical examination of Simon's model of certain distribution functions in linguistics. Applied Statistics, 2, 65-76.
62. Hill, B. M. (1970). Zipf's law and prior distributions for the composition of population. Journal of the American Statistical Association, 65, 1220-1232.
63. Hill, B. M. (1974). The rank-frequency form of Zipf's law. Journal of the American Statistical Association, 69, 1017-1026.
64. Hubert, J. J. (1978). A relationship between two forms of Bradford's law. Journal of the American Society for Information Science, 29, 159-161.
65. Hubert, J. J. (1981). General bibliometric models. Library Trends, 30, 65-81.
66. Irwin, J. O. (1963). The place of mathematics in medical and biological statistics. Journal of the Royal Statistical Society, Series A, 26, 1-45.
67. Irwin, J. O. (1968). The generalized Waring distribution applied to accident data. Journal of the Royal Statistical Society, Series A, 131, 205-225.
68. Irwin, J. O. (1975). The generalized Waring distribution: Part I, II, III. Journal of the Royal Statistical Society, Series A, 138, 18-31, 204-227, 374-384.
69. Kantor, P.B. (1978). A note on cumulative advantage distributions. Journal of the American Society for Information Science, 29, 202-204.
70. Karmeshu, N. C., Cano, N. C., & Lind, V. (1984). Rationales for Bradford's Law. Scientometrics, 6, 233-241.
71. Kendall, D. G. (1949). Stochastic processes and population growth. Journal of the Royal Statistical Society, Series A, 112, 230-264.
72. Kendall, M. G. (1960). The bibliography of operational research. Operational Research Quarterly, 11, 31-36.
73. Kendall, M. G. (1961). Natural law in the social sciences. Journal of the Royal Statistical Society, Series A, 124, 1-16.
74. Leimkuhler, F. F. (1967). The Bradford distribution. Journal of Documentation, 23, 197-207.
75. Leimkuhler, F. F. (1980). An exact formulation of Bradford's law. Journal of Documentation, 36, 285-292.
76. Leimkuhler, F. F. (1988). On bibliometric modeling. In L. Egghe & R. Rousseau (Eds.), Informetrics 87/88: Select proceedings of the First International Conference on Bibliometrics and Theoretical Aspects of Information Retrieval (pp. 97-104). Amsterdam: Elsevier.
77. Lotka, A. J. (1926). The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences, 16, 317-323. [cf. Fairthorne, R. A. (1969). Empirical hyperbolic distributions (Bradford-Zipf-Mandelbrot) for bibliometric description and prediction. Journal of Documentation, 25, 319-343.]
78. Lotka, A. J. (1926). The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences, 16, 317-323. [cf. Fairthorne, R. A. (1969). Empirical hyperbolic distributions (Bradford-Zipf-Mandelbrot) for bibliometric description and prediction. Journal of Documentation, 25, 319-343.]
79. Maia, M. J. F., & Maia, M. D. (1984). On the unity of Bradford's law. Journal of Documentation, 40, 206-216.
80. Mandelbrot, B. (1953). An information theory of the statistical structure of language. Proceedings of the Symposium on Applications of Communications Theory, London (pp. 486-500). London: Butterworths.
81. Mandelbrot, B. (1959). A note on a class of skew distribution functions: Analysis and critique of a paper by H. A. Simon. Information and Control, 2, 90-99.
82. Mandelbrot, B. (1961). Final note on a class of skew distribution functions: Analysis and critique of a model due to H. A. Simon. Information and Control, 4, 198-216.
83. Mandelbrot, B. (1965). Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Transactions on Communication Technology, 13, 71-90.
84. Morse, P. M. (1968). Library effectiveness: A systems approach. Cambridge, MA: MIT Press.
85. Morse, P. M. (1976). Demand for library materials: An exercise in probability analysis. Collection Management, 1, 47-78.
86. Morse, P. M. (1979). A queueing theory, Bayesian model for the circulation of books in a library. Operations Research, 27, 693-716.
87. Morse, P. M. (1981a). Implications of the exact Bradford distribution. Journal of the American Society for Information Science, 32, 43-50.
88. Morse, P. M. (1981b). The underlying characteristics of the Bradford distribution. Scientometrics, 3, 415-436.
89. Morse, P. M., & Leimkuhler, F. F. (1979). Exact solution for the Bradford distribution and its use in modeling informational data. Operations Research, 27, 187-198.
90. Naranan, S. (1970). Bradford's law of bibliography of science: An interpretation. Nature, 227, 631-632.
91. O'Neill, E. T. (1973). Limitations of Bradford's distributions. Proceedings of the ASIS Annual Meeting, 10, 177-178.
92. Oluić-Vuković, V. (1991). The shape of the distribution curve: An indication of changes in the journal productivity distribution pattern. Journal of Information Science, 17, 281-290.
93. Oluić-Vuković, V. (1992). Journal productivity distribution: Quantitative study of dynamic behaviour. Journal of the American Society for Information Science, 43, 412-421.
94. Oluić-Vuković, V. (1995). On the dynamic behavior of Bradford's law [Letter to the editor]. Journal of the American Society for Information Science, 46, 798-799.
95. Ord, K., & Patil, G. P. (1975). Statistical modelling: An alternative view. In G. P. Patil, S. Kotz, & J. K. Ord (Eds.), Statistical distributions in scientific work (Vol. 2, pp. 1-9). Dordrecht-Holland: D. Reidel.
96. Pareto, V. (1895). Cours d'economie politique. Vol. 2. Section 3. Lausanne, [cf. G. P. Patil, S. Kotz, & J. K. Ord (Eds.), Statistical distributions in scientific work (Vol. 2, pp. 1-9). Dordrecht-Holland: D. Reidel.]
97. Pareto, V. (1895). Cours d'economie politique. Vol. 2. Section 3. Lausanne, [cf. G. P. Patil, S. Kotz, & J. K. Ord (Eds.), Statistical distributions in scientific work (Vol. 2, pp. 1-9). Dordrecht-Holland: D. Reidel.]
98. Praunlich, P., & Kroll, M. (1978). Bradford's distribution: A new formulation. Journal of the American Society for Information Science, 29, 51-55.
99. Price, D. de S. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science, 27, 292-306.
100. Qiu, L. (1990). An empirical examination of the existing models for Bradford's law. Information Processing & Management, 26, 655-672.
101. Qiu, L., & Tague, J. (1990). Complete or incomplete data sets. The Groos droop investigated. Scientometrics, 19, 223-237.
102. Rao, I. K. R. (1980). The distribution of scientific productivity and social change. Journal of the American Society for Information Science, 31, 111-122.
103. Rao, I. K. R. (1990). Journal productivity in economics. In L. Egghe & R. Rousseau (Eds.), Informetrics 89/90: Select proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics (pp. 251-280). Amsterdam: Elsevier.
104. Rousseau, R. (1990). Relations between continuous versions of bibliometric laws. Journal of the American Society for Information Science, 41, 197-203.
105. Rousseau, R. (1994). Bradford curves. Information Processing & Management, 30, 267-277.
106. Schubert, A., & Glanzel, W. (1984). A dynamic look at a class of skew distributions. A model with scientometric applications. Scientometrics, 6, 149-167.
107. Schubert, A., & Telcs, A. (1989). Estimation of the publication potential in 50 U.S. states and in the District of Columbia based on the frequency distribution of scientific productivity. Journal of the American Society for Information Science, 40, 291-297.
108. Shokley, W. (1957). On the statistics of individual variation of productivity in research laboratories. Proceedings of IRE, 45, 279-290.
109. Sichel, H. S. (1975). On a distribution law for word frequencies. Journal of the American Statistical Association, 70, 542-547.
110. Sichel, H. S. (1985). A bibliometric distribution which really works. Journal of the American Society for Information Science, 36, 314-321.
111. Sichel, H. S. (1992). Anatomy of the generalized inverse Gaussian-Poisson distribution with special applications to bibliometric studies. Information Processing & Management, 28, 5-17.
112. Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425-440.
113. Simon, H. A. (1960). Some further notes on a class of skew distribution functions. Information and Control, 3, 80-88.
114. Simon, H. A. (1961). Reply to "Final note" by Benoit Mandelbrot. Information and Control, 4, 217-223.
115. Simon, H. A., & Van Wormer, T. A. (1963). Some Monte-Carlo estimates of the Yule distribution. Behavior Science, 17, 203-210.
116. Tabah, A. N., & Saber, A. J. (1990). Chaotic structures in informetrics. In L. Egghe & R. Rousseau (Eds.), Informetrics 89/90: Select proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics, London, Ontario, 1989 (pp. 281-289). Amsterdam: Elsevier.
117. Tague, J. (1981). The success-breeds-success phenomena and bibliometric processes. Journal of the American Society for Information Science, 32, 280-286.
118. Vlachy, J. (1980). Evaluating the distribution of individual performance. Scientia Yugoslavica, 6, 155-189.
119. Vlachy, J. (1994). Scientometrics - What to do? Scientometrics, 30, 521-527.
120. Vickery, B. C. (1948). Bradford's law of scattering. Journal of Documentation, 4, 198-203.
121. Wilkinson, E. A. (1972). The ambiguity of Bradford's law. Journal of Documentation, 28, 122-130.
122. Williams, E. B. (1943). The number of publications written by biologists. Annaly of Eugenics, 12, 143-144.
123. Willis, J. C. (1922). Age and areas: A study of geographical distribution and origin of species. Cambridge University Press, [cf. Yule, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philosophical Transactions of the Royal Society of London, Series B, 213, 21-87.]
124. Willis, J. C. (1922). Age and areas: A study of geographical distribution and origin of species. Cambridge University Press, [cf. Yule, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philosophical Transactions of the Royal Society of London, Series B, 213, 21-87.]
125. Yablonsky, A. I. (1980). On fundamental regularities of the distribution of scientific productivity. Scientometrics, 2, 3-34.
126. Yule, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis. Philosophical Transactions of the Royal Society of London, Series B, 213, 21-87.
127. Yule, G. U. (1944). A statistical study of vocabulary. London and New York: Cambridge University Press, [cf. Herdan, G. (1961). A critical examination of Simon's model of certain distribution functions in linguistics. Applied Statistics, 2, 65-76.]
128. Yule, G. U. (1944). A statistical study of vocabulary. London and New York: Cambridge University Press, [cf. Herdan, G. (1961). A critical examination of Simon's model of certain distribution functions in linguistics. Applied Statistics, 2, 65-76.]
129. Zipf, G. K. (1949). Human behaviour and the principle of least effort. Reading, MA: Addison-Wesley. [cf. Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425-440.]
130. Zipf, G. K. (1949). Human behaviour and the principle of least effort. Reading, MA: Addison-Wesley. [cf. Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425-440.]