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The families of probability distributions with heavy tails are considered one of the most essential continuous distributions that have broad uses in various areas of life, especially in areas related to economics, which is concerned with the subject of oil prices and securities, so the research was estimated two types of regression functions, represented by the multivariable parametric, non-parametric regression function, depending on the Matrix-Variate Variance Gamma(M-VVG) distribution and Matrix-Variate Normal Inverse Gaussian(M-VNIG) distribution for the error of models. As the multivariate non-parametric regression model was converted into a linear model based on the local polynomial smoother and through the classical method, multivariate Nadarya Watson smoother (NW-S) and the multivariate local linear smoother (LL-S) were obtained, as well as estimating the multivariate parametric regression function through the use of the maximum likelihood method (ML-M). The results were applied to actual data represented by Brent crude oil price data for the period from (2/11/2020) to (8/12/2020) measured in US dollars, and through the results of the Matlab programming and depending on the MSE standard, we note the superiority of the multivariate (NW-S) for the multivariate nonparametric regression function and for the error that follows a (M-VVG) distribution and for a Gauss kernel function, the value of the criterion was (MSE=0.2314), followed by the (M-VNIG) where the criterion (MSE=0.5601). The superiority of the identical error distributions for the multivariate parametric regression function, as well as the value of the criterion, was (MSE=0.4321,0.6433) respectively. [ABSTRACT FROM AUTHOR]