Applied Statistics Commons^™

On The Distribution Of Quadratic Expressions In Various Types Of Random Vectors, Ali Akbar Mohsenipour

Electronic Thesis and Dissertation Repository

Several approximations to the distribution of indefinite quadratic expressions in possibly singular Gaussian random vectors and ratios thereof are obtained in this dissertation. It is established that such quadratic expressions can be represented in their most general form as the difference of two positive definite quadratic forms plus a linear combination of Gaussian random variables. New advances on the distribution of quadratic expressions in elliptically contoured vectors, which are expressed as scalar mixtures of Gaussian vectors, are proposed as well. Certain distributional aspects of Hermitian quadratic expressions in complex Gaussian vectors are also investigated. Additionally, approximations to the distributions of …