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Sales distribution of consumer electronics


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  • Hisano, Ryohei
  • Mizuno, Takayuki
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    Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur quite often. The underlying sales dynamics found between both periods nicely matched a multiplicative process. However, even though the multiplicative term in the process displays a size-dependent relationship when a steady lognormal distribution holds, it shows a size-independent relationship when the power-law distribution holds. This difference in the underlying dynamics is responsible for the difference in the two observed distributions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 390 (2011)
    Issue (Month): 2 ()
    Pages: 309-318

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    Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:309-318

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    Keywords: Power-law distribution; Lognormal distribution; Multiplicative process; Sales distribution; Sales dynamics;


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    1. Rajeev Kohli & Raaj Sah, 2005. "Some Patterns of Market Shares of Brands Within and Across Product Categories," Working Papers 0604, Harris School of Public Policy Studies, University of Chicago.
    2. K. Sakai & T. Watanabe, 2010. "The firm as a bundle of barcodes," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 76(4), pages 507-512, August.
    3. Y. Malevergne & V. Pisarenko & D. Sornette, . "Gibrat’s law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal," Swiss Finance Institute Research Paper Series 09-40, Swiss Finance Institute.
    4. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005,
    5. O. S. Klass & O. Biham & M. Levy & O. Malcai & S. Solomon, 2007. "The Forbes 400, the Pareto power-law and efficient markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 143-147, 01.
    6. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    7. Joan Castillo, 1994. "The singly truncated normal distribution: A non-steep exponential family," Annals of the Institute of Statistical Mathematics, Springer, vol. 46(1), pages 57-66, March.
    8. Mizuno, Takayuki & Takayasu, Misako & Takayasu, Hideki, 2004. "The mean-field approximation model of company's income growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 403-411.
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    Cited by:
    1. Guo, Jinzhong & Xu, Qi & Chen, Qinghua & Wang, Yougui, 2013. "Firm size distribution and mobility of the top 500 firms in China, the United States and the world," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2903-2914.
    2. Fujimoto, S. & Ishikawa, A. & Mizuno, T. & Watanabe, T., 2011. "A New Method for Measuring Tail Exponents of Firm Size Distributions," Working Paper Series 7, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
    3. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics Discussion Papers 2011-29, Kiel Institute for the World Economy.
    4. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 5(20), pages 1-20.


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