Some Characteristics of Mahalanobis Distance for Bivariate Probability Distributions

Abstract

The standardized moments or Mahalanobis moments are easily calculated for bivariate elliptical distribution which includes bivariate normal and bivariate t-distributions as special cases. But these are challenging for many bivariate distributions. A set of alternative formulae is developed to derive Mahalanobis moments for any bivariate distribution. The second order Mahalanobis moment accounts for the coefficient of kurtosis. Ideas are illustrated with examples.