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Price index and its relation to the mean and median reference age

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  • L. Egghe

Abstract

This article consists of two parts. In the first part, we assume the simple decreasing exponential model for aging. In this case, we prove that the Price Index (the fraction of the references that are not older than a certain age) is a function of the mean reference age and also a function of the median reference age. Both functions are convexly decreasing, are 1 in 0 and tend to zero for the argument tending to infinity. In the second part, the more realistic lognormal aging model is used. We now show that the Price Index is not a pure function of the mean or median reference age, but a well‐defined relation in the form of a typical cloud of points. This cloud (as, e.g., discussed in a 1995 article of W. Glänzel & U. Schoepflin) is explained using results from probability theory and statistics. New data (about reference ages in Journal of the American Society for Information Science) are produced that confirm the theoretical findings. © 1997 John Wiley & Sons, Inc.

Suggested Citation

  • L. Egghe, 1997. "Price index and its relation to the mean and median reference age," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 48(6), pages 564-573, June.
    • Handle: RePEc:bla:jamest:v:48:y:1997:i:6:p:564-573
    DOI: 10.1002/(SICI)1097-4571(199706)48:63.0.CO;2-S
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    Cited by:

    1. Zhenyu Gou & Fan Meng & Zaida Chinchilla-Rodríguez & Yi Bu, 2022. "Encoding the citation life-cycle: the operationalization of a literature-aging conceptual model," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(8), pages 5027-5052, August.
    2. Urs Schoepflin & Wolfgang Glänzel, 2001. "Two decades of "Scientometrics". An interdisciplinary field represented by its leading journal," Scientometrics, Springer;Akadémiai Kiadó, vol. 50(2), pages 301-312, February.
    3. Anthony G. Stacey, 2021. "Ages of cited references and growth of scientific knowledge: an explication of the gamma distribution in business and management disciplines," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(1), pages 619-640, January.
    4. Ivan Jarić & Jelena Knežević-Jarić & Mirjana Lenhardt, 2014. "Relative age of references as a tool to identify emerging research fields with an application to the field of ecology and environmental sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 100(2), pages 519-529, August.
    5. Stacey, Anthony G, 2020. "Robust parameterisation of ages of references in published research," Journal of Informetrics, Elsevier, vol. 14(3).
    6. Richard Klavans & Kevin W. Boyack, 2008. "Thought leadership: A new indicator for national and institutional comparison," Scientometrics, Springer;Akadémiai Kiadó, vol. 75(2), pages 239-250, May.
    7. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    8. C. B. Amat & A. Yegros Yegros, 2009. "Median age difference of references as indicator of information update of research groups: A case study in Spanish food research," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(3), pages 447-465, March.
    9. Wang, Xianwen & Wang, Zhi & Mao, Wenli & Liu, Chen, 2014. "How far does scientific community look back?," Journal of Informetrics, Elsevier, vol. 8(3), pages 562-568.
    10. Yanhui Song & Feng Ma & Siluo Yang, 2015. "Comparative study on the obsolescence of humanities and social sciences in China: under the new situation of web," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 365-388, January.
    11. Pei-Shan Chi & Wolfgang Glänzel, 2022. "An article-based cross-disciplinary study of reference literature for indicator improvement," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(12), pages 7077-7089, December.
    12. L. Egghe, 2010. "A model showing the increase in time of the average and median reference age and the decrease in time of the Price Index," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 243-248, February.

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