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The inverse problem of multivariate and matrix-variate skew normal distributions |
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| Authors: | S Zheng J M Hardin |
| Institution: | 1. Department of Biostatistics and Epidemiology , East Tennessee State University , Box 70259, Johnson City , TN , 37614 , USA;2. Department of Finance , Nanjing Audit University , Nanjing , People's Republic of China;3. Department of Information Systems, Statistics, and Management Science , University of Alabama , Tuscaloosa , AL , 35487 , USA |
| Abstract: | In this paper, we prove that the joint distribution of random vectors Z 1 and Z 2 and the distribution of Z 2 are skew normal provided that Z 1 is skew normally distributed and Z 2 conditioning on Z 1 is distributed as closed skew normal. Also, we extend the main results to the matrix variate case. |
| Keywords: | skew normal distribution normal distribution conditional distribution multivariate distribution matrix variate skew normal distribution closed skew normal distribution matrix-variate closed skew normal distribution |