Doubly noncentral singular matrix variate beta distributions

Noncentral bimatrix variate generalised beta distributions

In this paper, we determine the density functions of nonsymmetrised doubly noncentral matrix variate beta type I and II distributions. The nonsymetrised density functions of doubly noncentral and noncentral bimatrix variate generalised beta type I and II distributions are also obtained.

Doubly singular matrix variate beta type I and II and singular inverted matricvariate $t$ distributions

In this paper, the densities of the doubly singular beta type I and II distributions are found, and the joint densities of their corresponding nonzero eigenvalues are provided. As a consequence, the density function of a singular inverted matricvariate t distribution is obtained.

A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications

The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of computers. Multiple sources in the literature deal with local approximations of the noncentral Wishart distribution with respect to its central counterpart. However, no source has yet developed explicit local approximations for the (central) Wishart distribution in terms of a normal analogue, which is important since Gaussian distributions are at the heart of th…

单位尺度双重奇异Beta Type II系综的最大有限根

Largest Finite Root of Identity-Scale Doubly Singular Beta Type II Ensembles

本文针对高维中双重奇异Beta Type II系综，证明其最大有限根恒等于非奇异q维Roy统计量，从而可直接用经典算法计算有限样本分布。