Main result of this paper is to derive the exact analytical expressions of information and covariance matrices for multivariate Burr III and logistic distributions. These distributions arise as tractable parametric models in price and income distributions, reliability, economics, Human population, some biological organisms to model agricultural population data and survival data. We showed that all the calculations can be obtained from one main moment multi dimensional integral whose expression is obtained through some particular change of variables. Indeed, we consider that this calculus technique for improper integral has its own importance .