2015/07/02 by Thomas Royen, Royen, Thomas
Mathematics · #60E15 #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical Inequalities and Applications #Probability (math.PR) #Statistical Distribution Estimation and Applications #math.PR #msc:60E15
paper · pdf · doi:10.48550/arxiv.1507.00528
10 pages
arxiv created 2015/07/02 · openalex publication_date 2015/07/02 · arxiv updated 2015/07/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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 of Krishnamoorthy and Parthasarathy [5]) with one degree of freedom. Its generalization to all integer degrees of freedom and sufficiently large non-integer "degrees of freedom" was recently proved in [10]. Here, this inequality is partly extended to smaller non-integer degrees of freedom and in particular - in a weaker form - to all infinitely divisible multivariate gamma distributions. A further monotonicity property - sometimes called "more PLOD (positively lower orthant dependent)" - for increasing correlations is proved for multivariate gamma distributions with integer or sufficiently large degrees of freedom.