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Predicting the long tail of book sales: Unearthing the power-law exponent

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  • Fenner, Trevor
  • Levene, Mark
  • Loizou, George

Abstract

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.

Suggested Citation

  • Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:12:p:2416-2421
    DOI: 10.1016/j.physa.2010.02.021
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    References listed on IDEAS

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    1. Erik Brynjolfsson & Yu (Jeffrey) Hu & Michael D. Smith, 2003. "Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers," Management Science, INFORMS, vol. 49(11), pages 1580-1596, November.
    2. Fenner, Trevor & Levene, Mark & Loizou, George, 2005. "A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 641-656.
    3. Judith Chevalier & Austan Goolsbee, 2003. "Measuring Prices and Price Competition Online: Amazon.com and BarnesandNoble.com," Quantitative Marketing and Economics (QME), Springer, vol. 1(2), pages 203-222, June.
    4. Derek De Solla Price, 1976. "A general theory of bibliometric and other cumulative advantage processes," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 27(5), pages 292-306, September.
    5. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    6. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
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    Cited by:

    1. Brabazon, Philip G & MacCarthy, Bart, 2012. "Investigating a long tail in retail vehicle sales," Omega, Elsevier, vol. 40(3), pages 302-313.
    2. Lozić, Joško & Milković, Marin & Fotova Čiković, Katerina, 2022. "The Impact Of The Long Tail Economy On The Business Result Of The Digital Platform: The Case Of Spotify And Match Group," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 13(1), pages 43-55.

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