Related papers: Matrix multinomial distribution
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
We consider in this paper the semiparametric mixture of two distributions equal up to a shift parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. In…
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…
This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…