The Mahalanobis distance and probability metrics

The purpose of this thesis is to examine two different concepts of distance between random variables which are the Mahalanobis distance and probability metrics. The thesis is divided into two parts. The first part deals with the Mahalanobis distance and its properties, distribution and moments. The first part concludes with a useful theorem which establishes the equivalence of the moments of different orders. The second part deals with probability metrics and reviews several well known probability metrics. This part concludes with a search for comparisons between the Mahalanobis distance and the Kantorovich-Rubinstein metric.