This note discusses elliptical distributions as well as their properties and provides a few applications. Firstly, basic concepts for multivariate random variables are being introduced. Besides the expectation and the covariance matrix the first part of the thesis deals with important numerical measures of association. After the Pearson product-moment correlation coefficient two rank correlation coefficients follow: Spearman's rho and Kendall's tau . Several properties of these three measures are being presented. They are applied for the analysis of a data set containing the daily returns of the Morgen Stanley Capital International (MSCI) indices of Germany, Europe, USA and North America from September 2005 to September 2010. In the second part of this note, a short motivation for the use of elliptical distributions in financial models is given. Initially, spherical distributions are introduced in order to be able to provide elliptical distributions and several of their properties afterwards. The relationship between this class of distributions and the well-known ones (for example the normal distribution) is shown. This thesis pays special attention to the relationship between rho and tau for elliptical random variables. It can be used to obtain a robust estimator for ?. Finally, two methods to transform non-positive semidefinite correlation matrices to positive semidefinite ones are being presented. These techniques are interesting because such non-positive semidefinite correlation matrices can occur estimating the correlation of a multivariate random variable based on the estimate of Kendall's tau . These concepts are illustrated by applying them to an example.      «

This note discusses elliptical distributions as well as their properties and provides a few applications. Firstly, basic concepts for multivariate random variables are being introduced. Besides the expectation and the covariance matrix the first part of the thesis deals with important numerical measures of association. After the Pearson product-moment correlation coefficient two rank correlation coefficients follow: Spearman's rho and Kendall's tau . Several properties of these three measures ar...     »