An alternative method for computing mean and covariance matrix of some multivariate distributions

Abstract

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating univariate integrals for computing the mean and covariance matrix of a multivariate normal distribution. Moment generating function technique is used for computing the mean and covariances between the elements of a Wishart matrix. In this article, an alternative method that uses matrix differentiation and differentiation of the determinant of a matrix is presented. This method does not involve any integration.

Keywords:

• mean vector
• covariance matrix
• multi-normal distribution
• Wishart distribution

Acknowledgement

The author thanks the management of Bharat Electronics for supporting this work.