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We construct the multivariate probability distributions (P\'olya, inverse P\'olya, hypergeometric and negative hypergeometric) from the generalized quantum algebra. Moreover, we derive the bivariate probability distributions and determine…

In this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also…

We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or…

Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…

In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the…

Correlated proportions appear in many real-world applications and present a unique challenge in terms of finding an appropriate probabilistic model due to their constrained nature. The bivariate beta is a natural extension of the well-known…

We prove the dispersive estimates for charge transfer Hamiltonians, including the matrix non-selfadjoint generalizations. The charge transfer models appear naturally in the study of stability of multi-soliton systems.

In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…

We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…

The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…

This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…

We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…

Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta…

In this article, we explore convolutions of distributions with distributions given by (weighted) line integration. We also explore the scattering of singularities of such convolutions.

We address two important statistical problems: that of estimating mixtures of multivariate normal distributions and mixtures of $t$-distributions based on univariate projections, and that of quantifying a discrepancy between mixture…

New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending…

Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…

A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…