Related papers: Differential relations for the largest root distri…
We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…
Recently, D. Wang has devised a new contour integral based method to simplify certain matrix integrals. Capitalizing on that approach, we derive a new expression for the probability density function (p.d.f.) of the joint eigenvalues of a…
We apply the holonomic gradient method introduced by Nakayama et al.(2011) to the evaluation of the exact distribution function of the largest root of a Wishart matrix, which involves a hypergeometric function 1F1 of a matrix argument.…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…