Related papers: Non-Central Multivariate Chi-Square and Gamma Dist…
In this paper, we determine the density functions of nonsymmetrised doubly noncentral matrix variate beta type I and II distributions. The nonsymetrised density functions of doubly noncentral and noncentral bimatrix variate generalised beta…
This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…
Let $\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\mathbf{W}=\mathbf{X}^H\mathbf{X}$, where $\mathbf{X}$ is $n\times m \, (n\geq m)$ complex Gaussian with non-zero mean $\boldsymbol{\Upsilon}$ and…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
This paper proposes a unified approach to enable the study of diverse distributions in the real, complex, quaternion and octonion cases, simultaneously. In particular, the central, nonsingular matricvariate and matrix multivariate Pearson…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality…
The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…
Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also…
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…
This paper proposes a generalisation of the Pearson type II distribution, which shall termed Pearson Type II-Riesz distribution, based in the Kotz-Riesz distribution. Specifically, the central nonsingular matricvariate generalised Pearson…
With any symmetric distribution $\mu$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+\delta)^2$, $\delta\not=0$, where $X$ is a random variable with distribution $\mu$. The…
We derive an integral expression $G(z)$ for the reciprocal gamma function, $1/\Gamma(z)=G(z)/\pi$, that is valid for all $z\in\mathbb{C}$, without the need for analytic continuation. The same integral avoids the singularities of the gamma…
We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest do not necessarily follow a chi-square distribution and take the…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…