Showing papers on "Multivariate gamma function published in 2017"
13 Nov 2017
TL;DR: In particular, the alternative hypotheses are not local ones as mentioned in this paper, and the condition n − 1 > p → ∞ suffices in their results under a big class of alternative hypotheses.
Abstract: Let Np(μ,Σ) be a p-dimensional normal distribution. Testing Σ equal to a given matrix or (μ,Σ) equal to a given pair through the likelihood ratio test (LRT) is a classical problem in the multivariate analysis. When the population dimension p is fixed, it is known that the LRT statistics go to χ2-distributions. When p is large, simulation shows that the approximations are far from accurate. For the two LRT statistics, in the high-dimensional cases, we obtain their central limit theorems under a big class of alternative hypotheses. In particular, the alternative hypotheses are not local ones. We do not need the assumption that p and n are proportional to each other. The condition n − 1 > p →∞ suffices in our results.
22 citations
TL;DR: In this article, the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector was studied and its asymptotic distribution as well as its approximate density was derived.
Abstract: In this paper we study the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector. We derive its asymptotic distribution as well as its approximate density fun ...
17 citations
TL;DR: In this article, the existence of non-central chi-square distributions and squared Bessel processes for positive semidefinite matrices with shape and noncentrality parameters is studied.
9 citations
TL;DR: In this paper, the rate of convergence to the unit of each of three newly introduced multivariate perturbed normalized neural network operators of one hidden layer is determined through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives.
Abstract: This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.
9 citations
TL;DR: The Wishart distribution is generalized utilizing a fresh approach that leads to the hypergeometric Wishart generator distribution with the Wisharts as special cases and a special case as a prior for the underlying matrix variate normal model.
3 citations
24 Apr 2017
TL;DR: Multivariate analogues of the extended gamma density, which will provide multivariate extensions to Tsallis statistics and superstatistics, can be obtained by making use of the pathway parameter β, and conditional density, best predictor function, regression theory, etc. are introduced.
Abstract: In this paper, I consider multivariate analogues of the extended gamma density, which will provide multivariate extensions to Tsallis statistics and superstatistics. By making use of the pathway parameter β , multivariate generalized gamma density can be obtained from the model considered here. Some of its special cases and limiting cases are also mentioned. Conditional density, best predictor function, regression theory, etc., connected with this model are also introduced.
3 citations
TL;DR: The numerical results verify that the newly proposed SE distributions fit the empirical distributions very well and the dimensions of Wishart matrix can be identified by the derivative of SE PDF.
Abstract: The eigenvalue distributions of complex Wishart matrices are critical research issues in random matrix theory (RMT). The scaled eigenvalue (SE) distributions of complex Wishart matrices with finite dimensions are deduced in this paper. The probability density function (PDF) and cumulative distribution function (CDF) of the SE are formulated in the closed-form and coefficient-based expressions. Moreover, the derivative of SE PDF is provided in an exact formulation utilizing the same coefficient vectors. The numerical results verify that the newly proposed SE distributions fit the empirical distributions very well and the dimensions of Wishart matrix can be identified by the derivative of SE PDF.
1 citations