# Some improved Gaussian correlation inequalities for symmetrical n-rectangles extended to some multivariate gamma distributions and some further probability inequalities

@article{Royen2020SomeIG, title={Some improved Gaussian correlation inequalities for symmetrical n-rectangles extended to some multivariate gamma distributions and some further probability inequalities}, author={T. Royen}, journal={arXiv: Statistics Theory}, year={2020} }

The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint MTP2-distribution (multivariate totally positive of order 2). Inequalities of the here given type hold at least for all MTP2-probability measures on R^n or (0,infinity)^n 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…

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