Properties and Estimations of a Multivariate Folded Normal Distribution

Xi Liu, Yiqiao Jin, Yifan Yang and Xiaoqing Pan ()
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Xi Liu: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Yiqiao Jin: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Yifan Yang: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Xiaoqing Pan: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Mathematics, 2023, vol. 11, issue 23, 1-15

Abstract: 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.

Keywords: multivariate folded normal distribution; marginal and conditional density functions; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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