Inhaltszusammenfassung

The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution function (cdf), which is MTP2 (multivariate totally positive of order 2). Inequalities of the given type hold at least for all MTP2-cdfs on Rx...xR or on (0,infinity)x...x(0,infinity) with everywhere positive smooth densities. In particular, at least some infinitely divisible multivariate chi-square distributions (gamma distributions in the sense ...The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution function (cdf), which is MTP2 (multivariate totally positive of order 2). Inequalities of the given type hold at least for all MTP2-cdfs on Rx...xR or on (0,infinity)x...x(0,infinity) with everywhere positive smooth densities. In particular, at least some infinitely divisible multivariate chi-square distributions (gamma distributions in the sense of Krishnamoorthy and Parthasarathy) with any positive real "degree od freedom" are shown to be MTP2. Moreover, further numerically calculable probability inequalities for a broader class of multivariate gamma distributions are derived. A differnet improvement for inequalities of the GCI-Type, and of a similar type with three instead of two groups of components with more special correlation structures is also obtained. The main idea behind these inequalities is to find for a given correlation matrix with positive correlations a further correlation matrix with smaller correlations whose inverse is an M-matrix and where the corresponding multivariate gamma cdf is numerically available.» weiterlesen» einklappen

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DFG Fachgebiet:
Mathematik

DDC Sachgruppe:
Mathematik