Classical distribution theory in higher dimensions is largely focused on the Gaussian distribution. However, for the Gaussian distribution it is well known that every marginal distribution, every conditional distribution and all linear transformations are also Gaussian. Besides, it is also obvious that these properties chosen individually are not sufficient conditions to characterize the Gaussian distribution. There are many non-Gaussian distributions which share some of these features with the Gaussian distribution. In the present talk we introduce couple of new theorems which characterizes the Gaussian distribution. Besides, one of the extensive application of the Gaussian distribution will be in classical classification theory. In the current note we also discusses the extensions of classical classification results to the theory of extreme value analysis. Problem in action: Let P and Q be a two sets of probability measures defined on the same sigma field. Let T be a transformation which maps every measure from P to one and only measure in Q. Now, given Q and T can we characterize the set P ?
School of Mathematical Sciences
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