This paper extends the work of Elal-Olivero (2010) on the alpha-skew normal distribution. The extension is a multivariate version of Elal-Olivero’s univariate case. Then we study the statistical properties of the new extension such as marginal and conditional distribution, closure under convolution with normal random variate. Furthermore, we illustrate the performance of the distribution using simulated data obtained from the generalized distribution via the Metropolis-Hasting algorithm.
Skew-normal Distribution, Skewness, Characteristics Function, Quadratic Form.
Department Mathematics and Statistics - La Trobe University - Victoria, 3086 - AUSTRALIA (email: firstname.lastname@example.org)
. School of Sciences - University of Southern Queensland - AUSTRALIA (e-mail: Shahjahan.Khan@usq.edu.au). Department of Statistics-Sultan Qaboos University - MUSCAT (e-mail: email@example.com). School of Medicine - University of Queensland - AUSTRALIA (e-mail: firstname.lastname@example.org).