Related papers: Doubly singular matrix variate beta type I and II …
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…
In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a…
We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings…
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 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…
The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the…
We study the one-dimensional Levy stable density distributions g(alpha, beta; x) for -infty < x < infty, for rational values of index alpha and the asymmetry parameter beta: alpha = l/k and beta = (l - 2r)/k, where l, k and r are positive…
In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…
In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
In this article, we study high-dimensional behavior of empirical spectral distributions $\{L_N(t), t\in[0,T]\}$ for a class of $N\times N$ symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic…
We construct a binary mutation invariant for skew-symmetric integer matrices. The invariant is not an integer congruence invariant for matrices of odd size: we provide examples of congruent such matrices with different values for the…
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
A new independence property of univariate beta distributions, related to the results of Kshirsagar and Tan for beta matrices, is presented. Conversely, a characterization of univariate beta laws through this independence property is proved.…
We show that a mixture of Beta distributions has log-concave density whenever the mixing weights are themselves log-concave. Some economic and statistical applications are provided in the last section.
In this paper, we study the alternating Euler $T$-sums and $\S$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of…