On multivariate truncated generalized Cauchy distribution

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• 作者：Saieed F. Ateya (1) (2)
  Elham A. Madhagi (3)
  
• 关键词：Generalized Cauchy distribution ; Moment generating function ; Mixed moments ; Correlation coefficient ; Skewness ; Kurtosis ; Maximum likelihood estimation ; Markov Chain Monte Carlo technique ; Monte Carlo integration ; 62F10 ; 62F15 ; 62N01 ; 62N02
• 刊名：Statistical Papers
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：54
• 期：3
• 页码：879-897
• 全文大小：447KB
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• 作者单位：Saieed F. Ateya (1) (2)
  Elham A. Madhagi (3)
  
  1. Department of Mathematics & Statistics, Taif University, Hawia, Taif, Saudi Arabia
  2. Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
  3. Department of Mathematics, Faculty of Education, Hodeidah University, Al Hudaydah, Yemen
  
• ISSN：1613-9798

文摘

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鈥揝mirnov (K鈥揝) test statistic to emphasize that the bivariate truncated generalized Cauchy model fits the data better than the other models.