Advances in statistical distribution theory inspired by communications systems

Abstract

This thesis contributes to statistical distribution theory by developing bivariate- and matrix variate distributions with their origins in the complex elliptical class. These contributions are inspired by the communications systems domain, where the underlying distribution is often assumed to be normal. By proposing the underlying distribution to be from the complex elliptical class allows the practitioner to assume different underlying distributions to alleviate the restriction of normality. The building blocks of the contributions in this thesis are systematically described and motivated. Through these advances and contributions within statistical distribution theory, proposed application within the communications systems field is presented. Key performance metrics are investigated under this complex elliptical assumption, and comparatively explored between two members, namely the normal and t.