Related papers: Bivariate Covariance Functions of P\'olya Type
Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
We point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the…
Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…
We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials…
The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo first constructed a global smooth irrotational solution…
The Bures metric and the associated Bures-Hall measure is arguably the best choice for studying the spectrum of the quantum mechanical density matrix with no apriori knowledge of the system. We investigate the probability of a gap in the…
Parity doublet model is an effective chiral model that includes the chiral variant and invariant masses of baryons. The chiral invariant mass has large impacts on the density dependence of models which can be constrained by neutron star…
We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the…
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…
Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…
By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…