相关论文: Kshirsagar--Tan independence property of beta matr…

In the paper we resolve positively the conjecture on a characterization of matrix Kummer and Wishart laws through independence property, which was posed in [Koudou, Statist. Probab. Lett. 82 (2012), 1903--1907] . Apart from the…

We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let $X$ and $Y$ be independent, non-degenerate random variables valued in $(0, \infty)$, then…

If $\alpha,\beta>0$ are distinct and if $A$ and $B$ are independent non-degenerate positive random variables such that $$S=\tfrac{1}{B}\,\tfrac{\beta A+B}{\alpha A+B}\quad \mbox{and}\quad T=\tfrac{1}{A}\,\tfrac{\beta A+B}{\alpha A+B} $$ are…

In this paper, the study of bivariate generalised beta type I and II distributions is extended to the complex matrix variate case, for which the corresponding density functions are found. In addition, for complex bimatrix variate beta type…

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…

Recently, Sasada and Uozumi (2024) investigated connections between classical (deterministic) and random integrable models, discovering a hierarchy of quadrirational Yang-Baxter independence preserving (IP) maps together with related…

In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let $X$ and $Y$ be independent, non-degenerate random variables with values in $(0,1)$, then $U=1-XY$ and $V=\frac{1-X}{U}$ are…

Well-known and newly developed renormalization schemes for $\tan\beta$ are analyzed in view of three desirable properties: gauge independence, process independence, and numerical stability in perturbation theory. Arguments are provided that…

Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…

Sasada and Uozumi, \cite{SasUoz2024}, identified independence preserving $[2:2]$ quadrirational parametric Yang-Baxter maps, see \eqref{YBEQ}, on $(0,\infty)$. In particular, the map denoted there by $H_{III,B}^{(\alpha,\beta)}$, see…

We show that the random matrix theory with non-integer "symmetry parameter" beta describes the statistics of transport parameters of strongly disordered two dimensional systems.

A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…

Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this…

Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…

A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of…

Renormalization schemes for tan(beta) are discussed in view of their gauge dependence. It is shown that several common renormalization schemes lead to a gauge-dependent definition of tan(beta), whereas two classes of gauge-independent…

It is well known Heyde's characterization of the Gaussian distribution on the real line: Let $\xi_1, \xi_2,\dots, \xi_n$, $n\ge 2,$ be independent random variables, let $\alpha_j, \beta_j$ be nonzero constants such that…

We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…