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On multivariate truncated generalized Cauchy distribution

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  • Saieed Ateya
  • Elham Madhagi

Abstract

In this paper, a multivariate form of truncated generalized Cauchy distribution (TGCD), which is denoted by (MVTGCD), is introduced. The joint density function, conditional density function, moment generating function and mixed moments of order $${b=\sum_{i=1}^{k}b_{i}}$$ are obtained. Making use of the mixed moments formula, skewness and kurtosis in case of the bivariate case are obtained. Also, all parameters of the distribution are estimated using the maximum likelihood and Bayes methods. A real data set is introduced and analyzed using three models. The first model is the bivariate Cauchy distribution, the second is the truncated bivariate Cauchy distribution and the third is the bivariate truncated generalized Cauchy distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic to emphasize that the bivariate truncated generalized Cauchy model fits the data better than the other models. Copyright Springer-Verlag 2013

Suggested Citation

  • Saieed Ateya & Elham Madhagi, 2013. "On multivariate truncated generalized Cauchy distribution," Statistical Papers, Springer, vol. 54(3), pages 879-897, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:879-897
    DOI: 10.1007/s00362-012-0467-9
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    References listed on IDEAS

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    1. Essam Al-Hussaini & Saieed Ateya, 2005. "Parametric estimation under a class of multivariate distributions," Statistical Papers, Springer, vol. 46(3), pages 321-338, July.
    2. Nadarajah Saralees, 2007. "A Truncated Bivariate t Distribution," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 303-313, January.
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    Cited by:

    1. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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