Skip to main content
Log in

Inventive productivity and the statistics of exceedances

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

We show that inventive productivity can be described by two variables, Frenquency and Lifetime. For several samples of inventors, we show that the Exponential and Generalized Pareto distributions provide excellent goodness-of-fit to these variables. Furthermore, good fits to these distributions arises naturally from the statistics of exceedance. Thus, a better theoretical foundation and connection to environmental variables is shown for Frequency and Lifetime than has been shown for Lotka's Law.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lotka, A. J., The Frequency of Distribution of Scientific Productivity,Journal of the Washington Acad. of Science, 16 (1926) 317–323.

    Google Scholar 

  2. Pao, M. L., An Empirical Examination of Lotka's Law,Journal of the American Society for Information Science, 37 (1986) 26–33.

    Article  Google Scholar 

  3. Leavens, D. H., Letter to the Editor,Econometrica, 21 (1953) 630–632.

    Google Scholar 

  4. Murphy, L. J., Lotka's Law in the Humanties?,Journal of the American Society for Information Science, 1 (1973) 461–462.

    MathSciNet  Google Scholar 

  5. Voos, H., Lotka and Information Science,Journal of the American Society for Information Science, 25 (1974) 270–272.

    Google Scholar 

  6. Pao, M. L., Bibliometrics and Computational Musicology,Collection Management, 3 (1979) 97–109.

    Article  MathSciNet  Google Scholar 

  7. Narin, F., Breitzman, A., Inventive Productivity,Research Policy, 24 (1995) 507–519.

    Article  Google Scholar 

  8. Huber, J. C., Invention and Inventivity as a Special Kind of Creativity, with Implications for General Creativity,Journal of Creative Behavior, 32 (1998a) 58–72.

    Google Scholar 

  9. Huber, J. C., Invention and Inventivity is a Random, Poisson Proces: A Potential Guide to Analysis of General Creativity,Creativity Research Journal, 11 (1998b) 1–241.

    Article  MathSciNet  Google Scholar 

  10. Mantell, L. H., On Laws of Special Abilities and the Production of Science Literature,American Documentation, 17 (1966) 8–16.

    Google Scholar 

  11. Sichel, H. S., A Bibliometric Distributions which Really Works,Journal of the American Society for Information Science, 36 (1985) 314–321.

    Google Scholar 

  12. Burrell, Q. L., Fenton, M. R., Yes, the GIGP Really Does Work— and is Workablel,Journal of the American Society for Information Science, 44 (1993) 61–69.

    Article  Google Scholar 

  13. Allison, P. D., Inequality and Scientific Productivity,Social Studies of Science, 10 (1980) 163–179.

    Google Scholar 

  14. Wagner-Döbler, R., Where has the Cumulative Advantage Gone? Some Observations about the Frequency Distribution of Scientific Productivity, of Duration of Scientific Participation, and of Speed of Publication,Scientometrics, 32 (1995) 123–132.

    Article  Google Scholar 

  15. Gupta, B. M., Karisiddappa, C. R., Productivity of Authors as Reflected by Duration of Their Scientific Participation and Speed of Publication,Scientometrics, 39 (1997) 281–291.

    Article  Google Scholar 

  16. McReynolds, P., Reliability of Ratings of Research Papers.American Psychologist, 26 (1971) 400–401.

    Article  Google Scholar 

  17. Zuckerman, H., Merton, R. K., Patterns of Evaluation in Science: Institutionalization, Structure and Functions of the Referee System,Minerva, 9 (1971) 66–100.

    Article  Google Scholar 

  18. Bowen, D. D., Perloff, R., Improving Manuscript Evaluation Procedures,American Psychologist, 27 (1972) 221–225.

    Article  Google Scholar 

  19. Mahoney, M. J., Publication Prejudices: An Experimental Study of Confirmatory Bias in the Peer Review System,Cognitive Theory and Research, 1 (1977) 161–175.

    Article  Google Scholar 

  20. Lindsey, D., Assessing Precision in the Manuscript Review Process: A Little Better than a Dice Roll,Scientometrics, 14 (1988) 75–82.

    Article  Google Scholar 

  21. Lindsey, D., Precision in the Manuscript Review Process: Hargens and Herting Revisited,Scientometrics, 22 (1991) 313–325.

    Article  Google Scholar 

  22. Hargens, L. L., Herting, J. R., Neglected Considerations in the Analysis of Agreement Among Journal RefereesScientometrics, 19 (1990), 91–106.

    Article  Google Scholar 

  23. U. S. Patent and Trademark Office, Manual of Patent Examining Procedure, U. S. Government Printing Office, Washington, DC, 1996.

    Google Scholar 

  24. Pelz, D. C., Andrews, F. M., Scientists in Organizations: Productive Climates for Research and Development. Institute for Social Research, The University of Michigan, Ann Arbor, MI, 1976.

    Google Scholar 

  25. Simonton, D. K.,Scientific Genius: A Psychology of Science. Cambridge University Press New York, 1988, p. 188.

    Google Scholar 

  26. Scott, S. G., Bruce, R. A., Determinants of Innovative Behavior: A Path Model of Individual Innovation in the Workplace.Academy of Management Journal, 37 (1994) 580–607.

    Article  Google Scholar 

  27. Amabile, T. M., Conti, R., Coon, H., Lazenby, J., Herron, M., Assessing the Work Environment for Creativity,Academy of Management Journal, 39, (1996), 1154–1184.

    Article  Google Scholar 

  28. Bennis, W., Cultivating Creative Genius, Industry Week, Aug 18 (1997) 84–88.

    Google Scholar 

  29. Mumford, M. D., Simonton, D. K., Creativity in the Workplace: People, Problems, and Structures,Journal of Creative Behavior, 31 (1997) 1–6.

    Google Scholar 

  30. Kanter, R. M., Kao, J., Wiersema, F.,Innovation: Breakthrough Thinking at 3M, DuPont, GE, Pfizer, and Rubbermaid, HarperCollins, New York, 1997, p. xv

    Google Scholar 

  31. Boorstin, D. J.The Americans: The Democratic Experience, Random House, New York, 1973.

    Google Scholar 

  32. Birr, K.,Pioneering in Industrial Research: The Story of the General Electric Research Laboratory. The Public Affairs Press, Washington, DC, 1957.

    Google Scholar 

  33. Broderick, J. T.,Willis Rodney Whitney: Pioneer of Industrial Research. Fort Organe Press, Albany NY, 1945.

    Google Scholar 

  34. Hasek, G., Manufacturing's Elite 100,Industry Week, Aug 17 (1998) 36–77.

    Google Scholar 

  35. Drucker, P. F.,Concept of the Corporation. The John Day Co., New York, 1946.

    Google Scholar 

  36. Drucker, P. F.,Concept of the Corporation (2nd ed.) The John Day Co, New York, 1972.

    Google Scholar 

  37. De Lorean, J. Z.,On a Clear Day You Can See General Motors, Wright Enterprises, Grosse Point, MI, 1979.

    Google Scholar 

  38. Hirshberg, J.,The Creative Priority: Driving innovative business in the real world. Harper Business, New York, 1998.

    Google Scholar 

  39. Huber, J. C., The Underlying Process Generating Lotka's Law and the Statistics of Exceedances,Information Processing & Management, 34 (1998c) 471–487.

    Article  Google Scholar 

  40. Huber, J. C., Cumulative Advantage and Success-Breeds-Success: The Value of Time Pattern Analysis,Journal of the American Society for Information Science, 49 (1998d) 471–476.

    Google Scholar 

  41. Schuster, E. F., Exchangability and Recursion in the Conditional Distribution Theory of Number and Length of Runs, InA. P. Godbole andS. G. Papastavridis (Eds.),Runs and Patterns in Probability: Selected Papers (pp. 91–118). Boston MA: Kluwer Academic Publishers, (1994) 91–118.

    Google Scholar 

  42. Hamburg, M.,Statistical Analysis for Decision Making. Harcourt, Brace, Jovanovich, New York, 1977.

    Google Scholar 

  43. Lehmann, E. L., D'Abrera, H. J. M.Nonparametrics: Statistical Methods Based on Ranks Holden-Day, San Francisco, 1975.

    MATH  Google Scholar 

  44. Brownlee, K. A.,Statistical Theory and Methodology: In Science and Engineering, John Wiley & Sons, New York, 1965.

    MATH  Google Scholar 

  45. Horner, K. L., Rushton, J. P., Vernon, P. A., Relation Between Aging and Research Productivity of Academic Psychologists,Psychology and Aging, 1 (1986) 319–324.

    Article  Google Scholar 

  46. McCrae, R. R., Arenberg, D., Costa Jr., P. T., Declines in Divergent Thinking With Age: Cross-Sectional, Longitudinal, and Cross-Sequential Analyses,Psychology and Aging, 2 (1987) 130–137.

    Article  Google Scholar 

  47. Simonton D. K., Creative Productivity: A Predictive and Explanatory Model of Career Trajectories and Landmarks,Psychological Review, 104 (1997) 66–89.

    Article  Google Scholar 

  48. Stephan, P. E., Levin, S. G.,Striking the Mother Lode in Science: The Importance of Age, Place, and Time. Oxford University Press, New York, 1992, p. 72.

    Google Scholar 

  49. Schubert, A., Glänzel, W., A Dynamic Look at a Class of Skew Distributions. A Model with Scientometric Applications,Scientometrics, 6 (1984) 149–167.

    Article  Google Scholar 

  50. Johnson, N. L., Kotz, S., Kemp, A. W.,Univariate Discrete Distributions (2nd ed.), John Wiley & Sons, New York, 1993.

    Google Scholar 

  51. D'Agostino, R. B., Graphical Analysis, InR. B. D'Agostino andM. A. Stephens (Eds),Goodness of Fit Techniques (pp. 461–496). New York: Marcel Dekker, (1986).

    Google Scholar 

  52. Klein, J. P., Moeschberger, M. L.,Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York, 1997 pp. 389–400.

    MATH  Google Scholar 

  53. Johnson, N. L., Kotz, S., Balakrishnan, N.,Continuous Univariate Distributions (2nd ed., Vol. 1). John Wiley & Sons, New York, 1994 p. 494.

    MATH  Google Scholar 

  54. Balakrishnan, N., Basu, A. P., (Eds.),The Exponential Distribution: Theory, Methods and Applications. Gordon and Breach, Amsterdam, 1995 p. 1.

    MATH  Google Scholar 

  55. Klein, J. P., Moeschberger, M. L.,Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York, 1997 p. 44.

    MATH  Google Scholar 

  56. Stephens, M. A., EDF Statistics for Goodness of Fit and Some Comparisons.Journal of the American Statistical Association, 69 (1974) 730–737.

    Article  Google Scholar 

  57. Stephens, M. A., Tests Based on EDF Statistics, InR. B. D'Agostino andM. A. Stephens (Eds.),Goodness of Fit Techniques (pp. 97–193). New York: Marcel Dekker, (1986).

    Google Scholar 

  58. Kaplan, E. L., Meier, P., Nonparametric Estimation from Incomplete Observations,Journal of the American Statistical Association 53 (1958) 457–481.

    Article  MATH  MathSciNet  Google Scholar 

  59. Parmar, M. K. B., Machin, D.,Survival Analysis: A Practical Approach, John Wiley & Sons, New York, 1995.

    MATH  Google Scholar 

  60. Crowder, M. J., Kimber, A. C., Smith, R. L., Sweeting, T. J.,Statistical Analysis of Reliability Data. Chapman & Hall, New York, 1991.

    Google Scholar 

  61. Klein, J. P., Moeschberger, M. L.,Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York, 1997 p. 84–96.

    MATH  Google Scholar 

  62. Johnson, N. L., Kotz, S., Balakrishnan, N.,Continuous Univariate Distributions (2nd ed., Vol. 1). John Wiley & Sons, New York, 1994, pp. 628–722.

    MATH  Google Scholar 

  63. Davis, H. T., Feldstein, M. L., The Generalized Pareto Law as a Model for Progressively Censored Survival Data,Biometrika, 66 (1979) 299–306.

    Article  MATH  MathSciNet  Google Scholar 

  64. Embrechts, P., Kluppelberg, C., Mikosch, T.,Modelling Extremal Events for Insurance and Finance Springer, Berlin, 1997 p. 294.

    MATH  Google Scholar 

  65. Pickands, J. III, Statistical Inference Using Extreme Order Statistics,The Annals of Statistics, 3 (1975) 119–131.

    MATH  MathSciNet  Google Scholar 

  66. Johnson, N. L., Kotz, S., Balakrishnan, N.,Continuous Univariate Distributions (2nd ed., Vol. 1). John Wiley & Sons, New York, 1994, pp. 614–620.

    MATH  Google Scholar 

  67. Embrechts, P., Kluppelberg, C., Mikosch, T.,Modelling Extremal Events for Insurance and Finance. Springer, Berlin, 1997, pp. 294–352.

    MATH  Google Scholar 

  68. Hosking, J. R. M., Wallis, J. R., Parameter and Quantile Estimation for the Generalized Pareto Distribution,Technometrics, 29 (1987) 339–349.

    Article  MATH  MathSciNet  Google Scholar 

  69. Drees, H., Refined Pickands Estimators with Bias Correction,Communications in Statistics–Theory and Methods, 25 (1996) 837–851.

    MATH  MathSciNet  Google Scholar 

  70. Li G., Doss, H., Generalized Pearson-Fisher Chi-Square Goodness-of-Fit Tests, with Applications to Models with Life History Data,The Annals of Statistics, 21 (1993) 772–797.

    MATH  MathSciNet  Google Scholar 

  71. Hawala, S., Wang, J.-L., A General Approach to Derive Chi-Square Type Goodness-of-Fit Tests for Lifetime Data, InN. P. Jewell, A. C. Kimber, Mei-Ling Ting Lee, andG. A. Whitmore (Eds.),Lifetime Data: Models in Reliability and Survival Analysis, (pp. 113–123). Boston, MA: Kluwer Academic., (1996).

    Google Scholar 

  72. Wang, personal communication, November 4, 1998.

  73. Koziol, J. A., Goodness-of-Fit Tests for Randomly Censored Data,Biometrika, 67 (1980) 693–696.

    Article  MATH  MathSciNet  Google Scholar 

  74. Michael, J. R., Schucany, W. R., Analysis of Data from Censored Samples, In:R. B. D'Agostino andM. A. Stephens (Eds.),Goodness of Fit Techniques (pp. 461–496). New York: Marcel Dekker, (1986).

    Google Scholar 

  75. Moore, D. S., Tests of Chi-Squared Type. InR. B. D'Agostino andM. A. Stephens (Eds.),Goodness of Fit Techniques (pp. 63–96). New York: Marcel Dekker, (1986).

    Google Scholar 

  76. Castillo, E., Hadi, A. S., Fitting the Generalized Pareto Distribution to Data,Journal of the American Statistical Association, 92 (1997) 1609–1620.

    Article  MATH  MathSciNet  Google Scholar 

  77. Castillo, personal communication, Aug. 6, 1998.

  78. Mitron Hirsch, N. D.,Genius and Creative Intelligence. Sci-Art Publishing, New York, 1931 pp. 235–236.

    Google Scholar 

  79. Rossman, J.,The Psychology of the Inventor: A Study of the Patentee. The Inventor's Publishing Co., Washington, DC, 1931 pp. 39–40.

    Google Scholar 

  80. MacKinnon, D. W., The Nature and Nurture of Creative Talent,American Psychologist, 17 (1962) 484–495.

    Article  Google Scholar 

  81. Levitt, T., Creativity Is Not Enough,Harvard Business Review, May–June (1963) 72–83.

    Google Scholar 

  82. Taylor, C. W., Barron, F. (Eds.),Scientific Creativity: Its Recognition and Development. John Wiley & Sons, New York, 1963 pp. 385–396.

    Google Scholar 

  83. Mackworth, N. H., Originality,American Psychologist, 20 (1965) 51–66.

    Article  Google Scholar 

  84. Telford, C. W., Sawrey, J. M.,The Exceptional Individual. Prentice-Hall, Englewood Cliffs, NJ, 1967 pp 191–192.

    Google Scholar 

  85. Wallas, G., Stages in the Creative Process. In:A. Rothenberg andC. R. Hausman (Eds.),The Creativity Question (pp. 69–73). Durham, NC, Duke University Press, (1976).

    Google Scholar 

  86. Austin, J. H.,Chase, Chance and Creativity; the Lucky Art of Novelty. Columbia University Press, New York, 1978 p. 112.

    Google Scholar 

  87. Barron, F., Harrington, D. M., Creativity, Intelligence and Personality,Annual Review of Psychology, 32 (1981) 439–476.

    Article  Google Scholar 

  88. Simonton, D. K.,Scientific Genius: A Psychology of Science, Cambridge University Press, New York, 1988 p. 64.

    Google Scholar 

  89. Drucker, P. F.,Post-Capitalist Society. Harper Business, New York, 1993, p. 49.

    Google Scholar 

  90. Gardner, H.,Frames of Mind: The Theory of Multiple Intelligences. Basic Books, New York, 1993 pp. 316–320.

    Google Scholar 

  91. Feldman, D. H., Csikszentmihalyi, M., Gardner, H.,Changing the World: A Framework for the Study of Creativity, Praeger Publishers, Westport, CT, 1994 pp. 22–23.

    Google Scholar 

  92. Florman, S. C.,The Existential Pleasures of Engineering. St. Martins Griffin, New York, 1994, p. 183.

    Google Scholar 

  93. Loehle, C., A Critical Path Analysis of Scientific Productivity,Journal of Creative Behavior, 28 (1994) 33–47.

    Google Scholar 

  94. Sternberg, R. J., Lubart, T. I.,Defying the Crowd: Cultivating Creativity in a Culture of Conformity. The Free Press, New York, 1995, pp. 283–288.

    Google Scholar 

  95. Amabile, T. M.,Greativity in Context. Harper Collins Publishers, New York, 1996 p. 98.

    Google Scholar 

  96. Sternberg, R. J.,Successful Intelligence: How Practical and Creative Intelligence Determine Success in Life. Simon & Schuster, New York, 1996, pp. 191–192.

    Google Scholar 

  97. Reiter-Palmon, R., Mumford, M. D., Boes, J. O., Runco, M. A., Problem Construction and Creativity: The Role of Ability, Cue Consistency, and Active Processing,Creativity Research Journal, 10 (1997) 9–23.

    Article  Google Scholar 

  98. Torrance, E. P.,Guiding Creative Talent, Robert E. Krieger Publishing Company, Huntinton, New York, 1976 reprint, original edition published by Prentice-Hall, Englewood Cliffs, NJ, 1963 p. 66.

    Google Scholar 

  99. Mansfield, R. S., Busse, T. V.,The Psychology of Creativity and Discovery. Nelson-Hill, Chicago, IL, 1981, p. 97.

    Google Scholar 

  100. Amabile, T. M., Gryskiewicz, S. S.,Creativity in the R&D Laboratory. Center for Creative Leadership, Greensboro, NC, 1987, p. 6.

    Google Scholar 

  101. Eisenberger, R., Learned Industriousness,Psychological Review, 99 (1992) 248–267.

    Article  Google Scholar 

  102. Abra, J.,The Motives for Creative Work: An Inquiry with Speculations about Sports and Religion. Hampton Press, Creeskill, NJ, 1997 p. 44.

    Google Scholar 

  103. Rushton, J. P., Murray, H. G., Paunnonen, S. V., Personality Characteristics Associated with High Research Productivity, In:D. N. Jackson andJ. P. Rushton (Eds.),Scientific Excellence: Origins and Assessment (pp. 129–148). Thousand Oaks, CA: Sage Publications, (1987).

    Google Scholar 

  104. May, R.,The Courage to Create. WW Norton, New York, 1975 p. 20.

    Google Scholar 

  105. Roe, A., A Psychological Study of Physical Scientists,Genetic Psychology Monographs, 43 (1951) 121–239.

    Google Scholar 

  106. Roe, A., A Psychologist Examines 64 Eminent Scientists,Scientific American, 187, Nov (1952) 21–25.

    Article  Google Scholar 

  107. Roe, A., A Psychological Study of Eminent Psychologists and Anthropologists, and a Comparison with Biological and Physical Scientists,Psychological Monographs: General and Applied, 67 (1953) 1–55.

    Google Scholar 

  108. Garfield, C.,Peak Performers. William Morrow, New York, 1986.

    Google Scholar 

  109. Getzels, J. W., Csikszentmihalyi, M., From Problem Solving to Problem Finding, InI. A. Taylor andJ. W. Getzels (Eds.),Perspectives in Creativity (pp. 90–116). Chicago: Aldine Publishing Co., (1975).

    Google Scholar 

  110. Couger, J. D.,Creative Problem Solving and Opportunity Finding. Boyd & Fraser, New York, 1995, p. 178.

    Google Scholar 

  111. Fry, A., The Post-It Notes Story,3M Today, Aug (1995) 3–5.

    Google Scholar 

  112. Gumbel, E. J.,Statistics of Extremes, Columbia University Press, New York, 1960.

    Google Scholar 

  113. Castillo, E.,Extreme Value Theory in Engineering. Academic Press, New York, 1988.

    MATH  Google Scholar 

  114. Price, D. J. D.,Little Science, Big Science. Columbia University Press, New York, 1963, p. 48.

    Google Scholar 

  115. Snedecor, G. W., Cochran, W. G.,Statistical Methods. (8th ed.), Iowa State University Press, Ames, IA, 1989 pp. 89–95.

    MATH  Google Scholar 

  116. Hamburg, M.,Statistical Analysis for Decision Making. Harcourt, Brace, Jovanovich, New York, 1977 p. 287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huber, J.C. Inventive productivity and the statistics of exceedances. Scientometrics 45, 33–53 (1999). https://doi.org/10.1007/BF02458467

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458467

Keywords

Navigation