Measures of dependence for the multivariate t distribution with applications to the stock market

Two measures of dependence for multivariate t and Cauchy random variables are developed based on Kullback–Leibler number. The mutual information number T(X) is obtained in a closed expression form, as well as its asymptotic distribution. A dependence coefficient ρ₁, is defined (based on the Kullback–Leibler number) with the properties of ρ₁=0 indicating independence and ρ₁=1indicating degeneracy. Two real life examples from the stock market are used to analyze the level of dependence and correlation among stocks.