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 measures is obtained by the special case with one degree of freedom.

A Note on Maximum and Minimum Stability of Certain Distributions

In the context of stability of the extremes of a random variable X with respect to a positive integer valued random variable N we discuss the cases (i) X is exponential (ii) non-geometric laws for N (iii) identifying N for the stability of a given X and (iv) extending the notion to a discrete random variable X.

Multivariate Log-Concave Distributions as a Nearly Parametric Model

In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions.

An Urn Model Approach for Deriving Multivariate Generalized Hypergeometric Distributions

We propose new generalized multivariate hypergeometric distributions, which extremely resemble the classical multivariate hypergeometric distributions. The proposed distributions are derived based on an urn model approach. In contrast to existing methods, this approach does not involve hypergeometric series.

On multivariate quasi-infinitely divisible distributions

A quasi-infinitely divisible distribution on $mathbb{R}^d$ is a probability distribution $mu$ on $mathbb{R}^d$ whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions on $mathbb{R}^d$. Equivalently, it can be characterised as a probability distribution whose characteristic function has a Levy--Khintchine type representation with a signed Levy measure, a so called quasi--Levy measure, rather than a Levy measure. A systematic study of such distributions in the univariate case has been carried out in Lindner, Pan and Sato cite{lindner}. The goal of the present paper is to collect some known results on multivariate quasi-infinitely divisible distributions and to extend some of the univariate results to the multivariate setting. In particular, conditions for weak convergence, moment and support properties are considered. A special emphasis is put on examples of such distributions and in particular on $mathbb{Z}^d$-valued quasi-infinitely divisible distributions.