On multivariate truncated generalized Cauchy distribution

Saieed Ateya () and Elham Madhagi ()

Statistical Papers, 2013, vol. 54, issue 3, 879-897

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

Keywords: 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 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-012-0467-9

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