Multivariate quadratic forms of random vectors


We obtain the distribution of the sum of n random vectors and the distribution of their quadratic forms: their densities are expanded in series of Hermite and Laguerre polynomials. We do not suppose that these vectors are independent. In particular, we apply these results to multivariate quadratic forms of Gaussian vectors. We obtain also their densities expanded in Mac Laurin series or in the form of an integral. By this last result, we introduce a new method of computation which can be much simpler than the previously known techniques. In particular, we introduce a new method in the very classical univariate case. We remark that we do not assume the independence of normal variables.Hermite polynomials Laguerre polynomials Fourier transforms Quadratic forms Gaussian vectors Moments

Similar works

Full text


Research Papers in Economics

Provided original full text link
Last time updated on 7/6/2012

This paper was published in Research Papers in Economics.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.