6 citations · 20 across the 9 of their papers we have counts for
10 papers
Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions
Dominic Edelmann, Donald Richards, Thomas Royen
The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full ge…
Some improved Gaussian correlation inequalities for symmetrical n-rectangles extended to some multivariate gamma distributions and some further probability inequalities
Thomas Royen
The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution (cdf) which is MTP2 (multivariate…
A Note on the Existence of the Multivariate Gamma Distribution
Thomas Royen
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 >…
Non-Central Multivariate Chi-Square and Gamma Distributions
Thomas Royen
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 an…
Some probability inequalities for multivariate gamma and normal distributions
Thomas Royen
The Gaussian correlation inequality for multivariate zero-mean normal probabilities of symmetrical n-rectangles can be considered as an inequality for multivariate gamma distributi…
The distribution of the square sum of Dirichlet random variables and a table with quantiles of Greenwood's statistic
Thomas Royen
The exact distribution of the square sum of Dirichlet random variables is given by two different univariate integral representations. Alternatively, three representations by orthog…