Information and Covariance Matrices for Multivariate Pareto (IV), Burr, and Related Distributions

Main result of this paper is to derive the exact analytical expressions of information and covariance matrix for multivariate Pareto, Burr and related distributions. These distributions arise as tractable parametric models in reliability, actuarial science, economics, finance and telecommunications. We showed that all the calculations can be obtained from one main moment multidimensional integral whose expression is obtained through some particular change of variables. Indeed, we consider that this calculus technique for that improper integral has its own importance.

Keywords:

gamma and beta functions , polygamma functions , Information matrix , covariance matrix , multivariate pareto models