Related papers: Multimatricvariate distribution under elliptical m…
Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme…
The eigenvalue distribution of Hoppe's two matrix model is investigated in detail as a function of the model's coupling. For small couplings it is a perturbed Wigner semicircle, while for large couplings it is a parabolic distribution which…
We investigate the product of $n$ complex non-Hermitian, independent random matrices, each of size $N\times N$ in the class of elliptic matrices, with independent identically distributed entries. The joint probability distribution of the…
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…
In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author's prior work, is specialized to the case of returns drawn from a multivariate Laplace…
The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and…
A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed…
Although cumulative family name distributions in many countries exhibit power-law forms, there also exist counterexamples. The origin of different family name distributions across countries is discussed analytically in the framework of a…
We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media.
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…
We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to ``star-shaped distributions'' with…
The value distribution of derivatives of characteristic polynomials of matrices from SO(N) is calculated at the point 1, the symmetry point on the unit circle of the eigenvalues of these matrices. We consider subsets of matrices from SO(N)…
We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…