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Tsallis statistics and gradually truncated Lévy flight—distribution of an economical index

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  • Gupta, Hari M.
  • Campanha, José R.

Abstract

Tsallis postulated a generalized form for entropy and give rise to a new statistics now known as Tsallis statistics. In the present work, we compare the Tsallis statistics with the gradually truncated Lévy flight, and discuss the distribution of an economical index—the Standard and Poor's 500—using the values of standard deviation as calculated by our model. We find that both statistics give almost the same distribution. Thus we feel that gradual truncation of Lévy distribution, after certain critical step size for describing complex systems, is a requirement of generalized thermodynamics or similar. The gradually truncated Lévy flight is based on physical considerations and bring a better physical picture of the dynamics of the whole system. Tsallis statistics gives a theoretical support. Both statistics together can be utilized for the development of a more exact portfolio theory or to understand better the complexities in human and financial behaviors. A comparison of both statistics is made.

Suggested Citation

  • Gupta, Hari M. & Campanha, José R., 2002. "Tsallis statistics and gradually truncated Lévy flight—distribution of an economical index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 381-387.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:3:p:381-387
    DOI: 10.1016/S0378-4371(02)00545-9
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    Cited by:

    1. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    2. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    3. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.

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