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

06/01/2020
by   Thomas Royen, et al.
0

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) with any positive real "degree of freedom" are shown to be MTP2. Moreover, further numerically calculable probability inequalities for a broad class of multivariate gamma distributions are derived and a different 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. 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 distribution function is numerically available.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/13/2022

Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions

The Gaussian product inequality is an important conjecture concerning th...
research
02/14/2022

Some New Inequalities for Beta Distributions

This note provides some new inequalities and approximations for beta dis...
research
08/15/2018

Characterization of multivariate distributions by means of univariate one

The aim of this paper is to show a possibility to identify multivariate ...
research
09/04/2018

Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization

In this paper, we study tail inequalities of the largest eigenvalue of a...
research
03/04/2021

Estimation of multivariate generalized gamma convolutions through Laguerre expansions

The generalized gamma convolutions class of distributions appeared in Th...
research
02/05/2020

On the mode and median of the generalized hyperbolic and related distributions

Except for certain parameter values, a closed form formula for the mode ...
research
03/22/2020

Proofs of non-optimality of the standard least-squares method for track reconstructions

It is a standard criterium in statistics to define an optimal estimator ...

Please sign up or login with your details

Forgot password? Click here to reset