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Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble


  • G. Oshanin
  • Yu. Holovatch
  • G. Schehr


We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha > 0 is the Pareto index and $\phi(x)$ is the cut-off function. We consider two forms of \phi(x): a bounded function \phi(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function \phi(x) = \exp(-L/x - x/H). In both cases \Psi(x) has moments of arbitrary order. We show that, for \alpha > 1, P(\omega) always has a unimodal form and is peaked at \omega = 1/2, so that most probably x_1 \approx x_2. For 0

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  • G. Oshanin & Yu. Holovatch & G. Schehr, 2011. "Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble," Papers 1106.4710,
  • Handle: RePEc:arx:papers:1106.4710

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    References listed on IDEAS

    1. Manski, Charles F., 2006. "Interpreting the predictions of prediction markets," Economics Letters, Elsevier, vol. 91(3), pages 425-429, June.
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    6. David S. Lee & Enrico Moretti, 2009. "Bayesian Learning and the Pricing of New Information: Evidence from Prediction Markets," American Economic Review, American Economic Association, vol. 99(2), pages 330-336, May.
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    8. Aseem Brahma & Sanmay Das & Malik Magdon-Ismail, 2010. "Comparing Prediction Market Structures, With an Application to Market Making," Papers 1009.1446,
    9. Marco Ottaviani & Peter Norman Sørensen, 2007. "Aggregation of Information and Beliefs in Prediction Markets," FRU Working Papers 2007/01, University of Copenhagen. Department of Economics. Finance Research Unit.
    10. Jie-Jun Tseng & Chih-Hao Lin & Chih-Ting Lin & Sun-Chong Wang & Sai-Ping Li, 2010. "Statistical properties of agent-based models in markets with continuous double auction mechanism," Papers 1002.0917,
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    Cited by:

    1. Eliazar, Iddo I. & Sokolov, Igor M., 2012. "Measuring statistical evenness: A panoramic overview," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1323-1353.

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