Department of Statistics, UCLA

Based on the reasoning expressed by Mahalanobis in his original article, the present article extends the Mahalanobis distance beyond the set of normal distributions. Sufficient conditions for existence and uniqueness are studied, and some properties derived. Since many statistical methods use the Mahalanobis distance as e vehicle, e.g. the method of least squares and the chi-square hypothesis test, extending the Mahalanobis distance beyond normal distributions yields a high ratio of output to input, since all those methods are immediately generalized beyond the normal distributions. Mahalanobis' idea also holds an immense conceptual beauty, mapping random variables into a frame of reference which ensures that apples are compared to apples.