摘要：Using di.erent types of polar and elliptical p olar coordinates, di.erent stochastic rep- resentations of the axis-aligned and the regular two-dimensional Gaussian distribution are derived. Advantages and disadvantages of these stochastic representations are dis- cussed. The non-Euclidean geometric measure representation of the axis-aligned two- dimensional Gaussian distribution in Richter (2011) is taken to derive a new geo- metric interpretation of the correlation co e.cient and to motivate a new geometric parametrization of the regular Gaussian law. Estimators of the new parameters and corresponding distributions are derived. A comparison with di.erent approaches from the literature shows the numerical stability of our results.
关键词：Sto chastic representations ; random coordinates ; maximum likeliho od ; estimation ; exact distributions ; correlation
