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The intensity of the random variable intercept in the sector of negative probabilities

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  • Marcin Makowski
  • Edward W. Piotrowski
  • Jan S{l}adkowski
  • Jacek Syska

Abstract

We consider properties of the measurement intensity $\rho$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a simple economic interpretation of this problem. This model is used to present the applicability of the method to the analysis of the negative probability on markets where there are anomalies in the law of supply and demand (e.g. Giffen's goods). It turns out that the new conditions to optimize the intensity $\rho$ require a new strategy. We propose a strategy (so-called $\grave{a}$ rebours strategy) based on the fixed point method and explore its effectiveness.

Suggested Citation

  • Marcin Makowski & Edward W. Piotrowski & Jan S{l}adkowski & Jacek Syska, 2015. "The intensity of the random variable intercept in the sector of negative probabilities," Papers 1503.07495, arXiv.org.
    • Handle: RePEc:arx:papers:1503.07495
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    References listed on IDEAS

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    1. Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2010. "Subjective modelling of supply and demand—the minimum of Fisher information solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4904-4912.
    2. Piotrowski, Edward W., 2003. "Fixed point theorem for simple quantum strategies in quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 196-200.
    3. Piotrowski, Edward W. & Sładkowski, Jan, 2002. "Quantum bargaining games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 391-401.
    4. Piotrowski, E.W. & Sładkowski, J., 2003. "The merchandising mathematician model: profit intensities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 496-504.
    5. Jankowski, Robert & Makowski, Marcin & Piotrowski, Edward W., 2014. "Parameter estimation by fixed point of function of information processing intensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 558-563.
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