Integrals and integral transformations related to the vector Gaussian distribution
https://doi.org/10.29235/1561-2430-2019-55-4-457-466
Abstract
This paper is dedicated to the integrals and integral transformations related to the probability density function of the vector Gaussian distribution and arising in probability applications. Herein, we present three integrals that permit to calculate the moments of the multivariate Gaussian distribution. Moreover, the total probability formula and Bayes formula for the vector Gaussian distribution are given. The obtained results are proven. The deduction of the integrals is performed on the basis of the Gauss elimination method. The total probability formula and Bayes formula are obtained on the basis of the proven integrals. These integrals and integral transformations could be used, for example, in the statistical decision theory, particularly, in the dual control theory, and as table integrals in various areas of research. On the basis of the obtained results, Bayesian estimations of the coefficients of the multiple regression function are calculated.
About the Authors
V. S. Mukha
Belarusian State University of Informatics and Radioelectronics
Russian Federation
Russian Federation
Vladimir S. Mukha – Dr. Sc. (Engineering), Professor, Professor of the Department of Information Technologies of Automated Systems.
6, P. Brovka Str., 220013, Minsk
N. F. Kako
Belarusian State University of Informatics and Radioelectronics
Russian Federation
Russian Federation
Nancy Farat Kako – Postgraduate Student
6, P. Brovka Str., 220013, Minsk
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