Properties and Estimations of a Multivariate Folded Normal Distribution

A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented.