Results 11 to 20 of about 17,290 (226)

Extended k-Gamma and k-Beta Functions of Matrix Arguments

Mathematics, 2020
Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented ...
Ghazi S. Khammash, Praveen Agarwal, Junesang Choi   +2 more
doaj   +2 more sources

Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions [PDF]

Transactions of the American Mathematical Society, 1987
Hypergeometric functions of matrix argument arise in a diverse range of applications in harmonic analysis, multivariate statistics, quantum physics, molecular chemistry, and number theory. This paper presents a general theory of such functions for real division algebras.
Kenneth I. Gross, Donald St. P. Richards
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Laplace approximations to hypergeometric functions of two matrix arguments

Journal of Multivariate Analysis, 2004
AbstractWe present a unified approach to Laplace approximation of hypergeometric functions with two matrix arguments. The general form of the approximation is designed to exploit the Laplace approximations to hypergeometric functions of a single matrix argument presented in Butler and Wood (Ann. Statist. 30 (2002) 1155, Laplace approximations to Bessel
Ronald W. Butler, Andrew T. A. Wood
openalex   +3 more sources

Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix

Journal of Multivariate Analysis, 2020
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the derivation of certain distributions for the eigenvalues of singular beta-Wishart matrices.
Koki Shimizu, Hiroki Hashiguchi
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Expressions for some hypergeometric functions of matrix argument with applications

Journal of Multivariate Analysis, 1975
AbstractReasonably simple expressions are given for some hypergeometric functions when the size of the argument matrix or matrices is two. Applications of these expressions in connection with the distributions of the latent roots of a 2 × 2 Wishart matrix are also given.
Robb J. Muirhead
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High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument [PDF]

Symmetry, 2011
Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups.
Donald St. P. Richards
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Total positivity, spherical series, and hypergeometric functions of matrix argument

Journal of Approximation Theory, 1989
AbstractGiven a totally positive function K of two real variables, is there a method for establishing the total positivity of K in an “obvious” fashion? In the case in which K(x, y) = f(xy), where f is real-analytic in a neighborhood of zero, we obtain integral representations for the determinants which define the total positivity of K.
Kenneth I. Gross, Donald St. P. Richards
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Hypergeometric functions of matrix arguments and linear statistics of multi-spiked Hermitian matrix models

Journal of Multivariate Analysis, 2015
This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a central Wishart ensemble with fixed-rank perturbation of the identity matrix, the second is a non-central Wishart
Damien Passemier, Matthew R. McKay, Yang Chen   +2 more
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Eigenvalue distributions of beta-Wishart matrices [PDF]

, 2014
We derive explicit expressions for the distributions of the extreme eigenvalues of the beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex
A. Edelman, Plamen Koev
semanticscholar   +3 more sources

Hypergeometric Functions: From One Scalar Variable to Several Matrix Arguments, in Statistics and Beyond

Open Journal of Statistics, 2016
Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in ...
T. Pham‐Gia, Dinh Ngoc Thanh
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