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An intermediate distribution between Gaussian and Cauchy distributions


  • Liu, Tong
  • Zhang, Ping
  • Dai, Wu-Sheng
  • Xie, Mi


In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.

Suggested Citation

  • Liu, Tong & Zhang, Ping & Dai, Wu-Sheng & Xie, Mi, 2012. "An intermediate distribution between Gaussian and Cauchy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5411-5421.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5411-5421
    DOI: 10.1016/j.physa.2012.06.035

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    Cited by:

    1. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259, September.
    2. Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.


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