On a formula for the h-index

Journal of Informetrics

Volumn 9, Issue 4, 2015, Pages 762-776

  Bertoli Barsotti, Lucio ^a   Lando, Tommaso ^b  

^a UNIVERSITY OF BERGAMO   (Italy)

^b VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

Author keywords

Citation data; Citation statistic; Geometric distribution; H Index; Lambert W function

Indexed keywords

INDEXING (OF INFORMATION);

AVERAGE ABSOLUTE ERROR; BIBLIOMETRIC INDICATORS; CITATION DATA; EMPIRICAL STUDIES; GEOMETRIC DISTRIBUTION; H INDICES; LAMBERT W FUNCTION; PREDICTIVE FORMULAS;

PROBABILITY DISTRIBUTIONS;

EID: 84940532440     PISSN: 17511577     EISSN: 18755879     Source Type: Journal    
DOI: 10.1016/j.joi.2015.07.004     Document Type: Article

References (65)

1. Abbas A.M. Bounds and inequalities relating h-index, g-index, e-index and generalized impact factor: An improvement over existing models. PLoS ONE 2012, 7(4):e33699. 10.1371/journal.pone.0033699.
2. Adler R., Ewing J., Taylor P. Citation statistics. Statistical Sciences 2009, 24(1):1-14.
3. Anastasiadis A.D., deAlbuquerque M.P., deAlbuquerque M.P., Mussi D.B. Tsallis q-exponential describes the distribution of scientific citations-A new characterization of the impact. Scientometrics 2010, 83(1):205-218.
4. Anderegg W.R.L., Prall J.W., Harold J., Schneider S.H. Expert credibility in climate change. Proceedings of the National Academy of Sciences 2010, 107:12107-12109.
5. Arnold B.C. Pareto distributions 1983, International Cooperative Publishing House, Fairland, MD.
6. Bertoli-Barsotti L. Improving a decomposition of the h-index. Journal of the American Society for Information Science and Technology 2013, 64(7):1522.
7. Bertoli-Barsotti L., Lando T. A geometric model for the analysis of citation distributions. International Journal of Mathematical Models and Methods in Applied Sciences 2015, 9:315-319.
8. Bletsas A., Sahalos J.N. Hirsch index rankings require scaling and higher moment. Journal of the American Society for Information Science and Technology 2009, 60:2577-2586.
9. Burrell Q.L. Hirsch's h-index: A stochastic model. Journal of Informetrics 2007, 1(1):16-25.
10. Burrell Q.L. Extending Lotkaian informetrics. Information Processing and Management 2008, 44(5):1794-1807.
11. Burrell Q.L. The h-index: A case of the tail wagging the dog?. Journal of Informetrics 2013, 7:774-783.
12. Burrell Q.L. Formulae for the h-index: A lack of robustness in Lotkaian informetrics?. Journal of the American Society for Information Science and Technology 2013, 64(7):1504-1514.
13. Burrell Q.L. The individual author's publication-citation process: Theory and practice. Scientometrics 2014, 98(1):725-742.
14. Campanario J.M. Distribution of ranks of articles and citations in journals. Journal of the Association for Information Science and Technology 2010, 61(2):419-423.
15. Csajbók E., Berhidi A., Vasas L., Schubert A. Hirsch-index for countries based on essential science indicators data. Scientometrics 2007, 73:91-117.
16. de Solla Price D. A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science 1976, 27(5):292-306.
17. Egghe L. Power laws in the information production process: Lotkaian informetrics 2005, Academic Press, London.
18. Egghe L. Relations between the continuous and the discrete Lotka power function. Journal of the American Society for Information Science and Technology 2005, 56(7):664-668.
19. Egghe L., Rousseau R. An informetric model for the Hirsch-index. Scientometrics 2006, 69(1):121-129.
20. Egghe L., Rousseau R. The Hirsch index of a shifted Lotka function and its relation with the impact factor. Journal of the American Society for Information Science and Technology 2012, 63(5):1048-1053.
21. Egghe L., Guns R., Rousseau R. Thoughts on uncitedness: Nobel laureates and fields medalists as case studies. Journal of the American Society for Information Science and Technology 2011, 62(8):1637-1644.
22. Glänzel W. On the h-index-A mathematical approach to a new measure of publication activity and citation impact. Scientometrics 2006, 67(2):315-321.
23. Glänzel W. Characteristic scores and scales. Journal of Informetrics 2007, 1:92-102.
24. Glänzel W. On some new bibliometric applications of statistics related to the h-index. Scientometrics 2008, 77(1):187-196.
25. Hirsch J.E. An index to quantify an individual's scientific research output. Proceedings of the National Academy of Sciences of the United States of America 2005, 102(46):16569-16572.
26. Hirsch J.E. Does the h index have predictive power?. Proceedings of the National Academy of Sciences of the United States of America 2007, 104(49):19193-19198.
27. Iglesias J., Pecharroman C. Scaling the h-index for different scientific ISI fields. Scientometrics 2007, 73(3):303-320.
28. Johnson N.L., Kotz S., Balakrishnan N. Continuous univariate distributions 1994, Vol. 1. Wiley, New York, NY. 2nd ed.
29. Johnson N.L., Kemp A.W., Kotz S. Univariate discrete distributions 2005, Wiley, New York. 3rd ed.
30. Lafouge T. The source-item coverage of the exponential function. Journal of Informetrics 2007, 1(1):59-67.
31. Laherrère J.H. Distributions de type fractal parabolique dans la Nature. Comptes Rendus de l'Academie des Sciences 1996, T.322(Série IIa n. 7):535-541.
32. Laherrère J., Sornette D. Stretched exponential distributions in nature and economy: "Fat tails" with characteristic scales. European Physical Journal B 1998, 2(4):525-539.
33. Lancho-Barrantes B.S., Guerrero-Bote V.P., Moya-Anegon F. The iceberg hypothesis revisited. Scientometrics 2010, 85(2):443-461.
34. Lando T., Bertoli-Barsotti L. A new bibliometric index based on the shape of the citation distribution. PLoS ONE 2014, 9(12):e115962. 10.1371/journal.pone.0115962.
35. Malacarne L.C., Mendes R.S., Lenzi E.K. q-Exponential distribution in urban agglomeration. Physical Review E 2001, 65:017106.
36. Malesios C. Some variations on the standard theoretical models for the h-index: A comparative analysis. Journal of the Association for Information Science and Technology 2015, 10.1002/asi.23410.
37. Mansilla R., Köppen E., Cocho G., Miramontes P. On the behavior of journal impact factor rank-order distribution. Journal of Informetrics 2007, 1:155-160.
38. Martinez-Mekler G., Martinez R.A., del Rio M.B., Mansilla R., Miramontes P., Cocho G. Universality of rank-ordering distributions in the arts and sciences. PLoS ONE 2009, 4:e4791.
39. Mingers J., Burrell Q.L. Modeling citation behavior in Management Science journals. Information Processing and Management 2006, 42:1451-1464.
40. Nicholls P.T. Estimation of Zipf parameters. Journal of the American Society for Information Science 1987, 38:443-445.
41. Perc M. Zipf's law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia's research as an example. Journal of Informetrics 2010, 4:358-364.
42. Petersen A.M., Stanley H.E., Succi S. Statistical regularities in the rank-citation profile of scientists. Scientific Reports 2011, 1:181. 10.1038/srep00181.
43. Prathap G. Is there a place for a mock h-index?. Scientometrics 2010, 84:153-165.
44. Prathap G. The 100 most prolific economists using the p-index. Scientometrics 2010, 84:167-172.
45. Prathap G. The Zynergy-index and the formula for the h-index. Journal of the Association for Information Science and Technology 2014, 65(2):426-427.
46. Radicchi F., Fortunato S., Castellano C. Universality of citation distributions: Toward an objective measure of scientific impact. Proceedings of the National Academy of Sciences 2008, 105(45):17268-17272.
47. Redner S. How popular is your paper?. An empirical study of the citation distribution. The European Physical Journal B 1998, 4:131-134.
48. Redner S. Citation statistics from 110 years of physical review. Physics Today 2005, 58(1):49-54.
49. Rousseau B., Rousseau R. LOTKA: A program to fit a power law distribution to observed frequency data. Cybermetrics 2000, 4(1)
50. Schubert A., Glänzel W. A systematic analysis of Hirsch-type indices for journals. Journal of Informetrics 2007, 1:179-184.
51. Schubert A., Korn A., Telcs A. Hirsch-type indices for characterizing networks. Scientometrics 2009, 78(2):375-382.
52. Shalizi R.C. Maximum likelihood estimation for q-exponential (Tsallis) distributions 2007, (ar***X***iv:math/0701854v2).
53. Stringer M.J., Sales-Pardo M., Amaral L.A.N. Effectiveness of journal ranking schemes as a tool for locating information. PLoS ONE 2008, 3(2):e1683.
54. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics 1988, 52:479.
55. Tsallis C., de Albuquerque M.P. Are citations of scientific papers a case of nonextensivity?. European Physical Journal B 2000, 13(4):777-780.
56. van Raan A.F.J. Two-step competition process leads to quasi power law income distribution. Application to scientific publication and citation distribution. Physica A 2001, 298:530-536.
57. van Raan A.F.J. Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgment for 147 chemistry research groups. Scientometrics 2006, 67(3):491-502.
58. Vinkler P. The π-index: A new indicator for assessing scientific impact. Journal of Information Science 2009, 35:602-612.
59. Vinkler P. The π-index: A new indicator to characterize the impact of journals. Scientometrics 2010, 82(3):461-475.
60. Wallace M.L., Larivière V., Gingras Y. Modeling a century of citation distributions. Journal of Informetrics 2009, 3(4):296-303.
61. Weibull W. A statistical distribution of wide applicability. Journal of Applied Mechanics 1951, 18:293-297.
62. Wolfram Research Inc. Wolfram Mathematica 2013, Documentation Center, 〈http://reference.wolfram.com/language/ref/ProductLog.html〉 (ProductLog).
63. Wolfram Research Inc. Mathematica, Version 9.0 2012, Wolfram Research, Inc., Champaign, IL.
64. Ye F.Y. An investigation on mathematical models of the h-index. Scientometrics 2009, 81:493-498.
65. Ye F.Y. A unification of three models for the h-index. Journal of the American Society for Information Science and Technology 2011, 62(1):205-207.