• Corpus ID: 219177169

# 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}
}
• T. Royen
• Published 1 June 2020
• Mathematics
• arXiv: Statistics Theory
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…

## References

SHOWING 1-10 OF 29 REFERENCES
Some upper tail approximations for the distribution of the maximum of correlated chi-square or gamma random variables
• Far East J. Theor. Stat
• 2013
Some probability inequalities for multivariate gamma and normal distributions
The Gaussian correlation inequality for multivariate zero-mean normal probabilities of symmetrical n-rectangles can be considered as an inequality for multivariate gamma distributions (in the sense
A Note on the Existence of the Multivariate Gamma Distribution
The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special
Non-Central Multivariate Chi-Square and Gamma Distributions
A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank.
ON TP2 AND LOG-CONCAVITY
• Mathematics
• 2016
Inter-relations between the TP2 property and log-concavity of density functions have been investigated. The general results are then applied to noncentral chi-square density functions and beta
A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability
A survey on multivariate chi-square distributions and their applications in testing multiple hypotheses
• Mathematics
• 2014
We are concerned with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several
Some representations for convolutions of multivariate gamma distributions
• Far East J. Theor. Stat
• 2013
Integral Representations and Approximations for Multivariate Gamma Distributions
AbstractLet R be a p×p-correlation matrix with an “m-factorial” inverse R−1 = D − BB′ with diagonal D minimizing the rank m of B. A new $$\left(m+1 \atop 2\right)$$-variate integral representation is