Elliptical distribution

rdf:langString Elliptical distribution

rdf:langString In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution is used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t-distribution, or light (in comparison with the normal distribution). Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are also used in robust statistics to evaluate proposed multivariate-statistical procedures.