On moments of truncated multivariate normal/independent distributions

Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate t, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository.

Automated summary

This paper derives explicit expressions for the moments of truncated multivariate normal/independent distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is conducted to validate the proposed formulae for five selected members of the distributions.