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In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
This paper derives the elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation is proposed, instead of the independent element by element…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
This paper studies new Lancaster characterizations of bivariate multivariate Poisson, negative binomial and normal distributions which have diagonal expansions in multivariate orthogonal polynomials. The characterizations extend classical…
We collect here elementary properties of differentiation matrices for univariate polynomials expressed in various bases, including orthogonal polynomial bases and non-degree-graded bases such as Bernstein bases and Lagrange \& Hermite…
A multivariate extension of the Dickman distribution was recently introduced, but very few properties have been studied. We discuss several properties with an emphasis on simulation. Further, we introduce and study a multivariate extension…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…