Related papers: Distribution theory of quadratic forms with matrix…
This paper introduces four matrix normal distributions on analytic bundles of flag varieties, extending the separable covariance $\varPhi \otimes \varPsi$ with potentially variable-level ($\varPsi$) and/or sample-level ($\varPhi$)…
The solution of $ X=AX+1 $ is analyzed for a discrete variable $ A $ with $ \mathbb{P}\left[A=0\right]>0 $. Accordingly, a fast algorithm is presented to calculate the obtained heavy tail density. To exemplify, the compound product…
We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…
Given a number field $k$ and a finitely generated subgroup $\mathcal{A} \subseteq k^*$, we study the distribution of $S_4$-quartic extensions of $k$ such that the elements of $\mathcal{A}$ are norms. We show that the density of such…
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
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…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
Given any fixed $N \times N$ positive semi-definite diagonal matrix $G\ge 0$ we derive the explicit formula for the density of complex eigenvalues for random matrices $A$ of the form $A=U\sqrt{G}$} where the random unitary matrices $U$ are…
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion.…
We show that the density $\mu$ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities $\mu_{p^s}$ of SNF over $\mathbb{Z}/p^s\mathbb{Z}$ with $p$ a prime and $s$ some positive integer. Our…
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…
In this paper, a general class of mixture of some densities is proposed. The proposed class contains some of classical and weighted distributions as special cases. Formulas for each of cumulative distribution function, reliability function,…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
Input-output, growth-decay, production-consumption type situations abound in many practical problems. When the input and output variables are independently gamma distributed, various aspects of the residual effect are already tackled by the…
This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith…
The canonical form of scale mixtures of multivariate skew-normal distribution is defined, emphasizing its role in summarizing some key properties of this class of distributions. It is also shown that the canonical form corresponds to an…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…