Related papers: Singular matrix variate Birnbaum-Saunders distribu…

A probabilistic representation for a class of weighted $p$-radial distributions, based on mixtures of a weighted cone probability measure and a weighted uniform distribution on the Euclidean $\ell_p^n$-ball, is derived. Large deviation…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

An elliptic random matrix $X$ is a square matrix whose $(i,j)$-entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{ji}$. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with…

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Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in…

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…

For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or…

In this paper, we introduce a bivariate exponentaited generalized Weibull-Gompertz distribution. The model introduced here is of Marshall-Olkin type. Several properties are studied such as bivariate probability density function and it is…

We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of Schur-Hadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSDs of…

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…

In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…

We consider a generalization of the inverse problem of the electrocardiography in the framework of the theory of elliptic and parabolic differential operators. More precisely, starting with the standard bidomain mathematical model related…

We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1F_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions…

We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…

The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…