Related papers: Multivariate normal distribution for integral poin…
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…
In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…
In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…
We develop a global arithmetic framework for studying endomorphism rings inside ordinary elliptic isogeny classes over finite fields. Let p be a prime and let I(t,p) be an ordinary isogeny class over the finite field F_p with Frobenius…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We…
In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…
We show that on a metric graph of genus $g$, a divisor of degree $n$ generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass…
An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss.
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.
In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties,…