Showing papers on "Multivariate gamma function published in 2011"
TL;DR: In this paper, a unified approach that enables the Wishart distribution to be studied simultaneously in real, complex, quaternion and octonion cases under elliptical models was proposed.
51 citations
TL;DR: In this article, the first and second moments of the Moore-Penrose generalized inverse of a singular standard Wishart matrix were derived without relying on a density, using the moments of an inverse Wishart distribution and an invariance argument related to the literature on tensor functions.
Abstract: We derive the first and the second moments of the Moore-Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.
40 citations
TL;DR: Consistent goodness-of-fit tests are proposed for symmetric and asymmetric multivariate Laplace distributions of arbitrary dimension that result in computationally convenient representations and a limit value of these test statistics is obtained when this weight function approaches a Dirac delta function.
18 citations
1 Jan 2011
TL;DR: In this paper, the density functions associated with the multivariate gamma and beta distributions were obtained and used to obtain the expectations involving the multivariable H-function of multivariate H-functions.
Abstract: The aim of this paper is to obtain some density functions associated with the multivariate gamma and beta distributions and use their applications to obtain the expectations involving the multivariable H-function. Finally, we also derive the moments for these multivariate beta and gamma distributions and also discussed their special cases. The results derived here are quite general in nature and capable of yielding a very large number of results (new and known) hitherto scattered in the literature.
1 citations
TL;DR: In this paper, a class of multivariate bilateral selection t distributions is proposed for analyzing non-normal (skewed and/or bimodal) multivariate data.
Abstract: This article proposes a class of multivariate bilateral selection t distributions useful for analyzing non-normal (skewed and/or bimodal) multivariate data. The class is associated with a bilateral selection mechanism, and it is obtained from a marginal distribution of the centrally truncated multivariate t. It is flexible enough to include the multivariate t and multivariate skew-t distributions and mathematically tractable enough to account for central truncation of a hidden t variable. The class, closed under linear transformation, marginal, and conditional operations, is studied from several aspects such as shape of the probability density function, conditioning of a distribution, scale mixtures of multivariate normal, and a probabilistic representation. The relationships among these aspects are given, and various properties of the class are also discussed. Necessary theories and two applications are provided.
TL;DR: In this article, a new probability density function associated with a Bessel function is introduced, which is the generalization of a gamma-type distribution, and suitability of this density as a good model in Bayesian inference and regression theory is also discussed.
Abstract: A new probability density function associated with a Bessel function is introduced, which is the generalization of a gamma-type distribution. Some of its special cases are also mentioned. Multivariate analogue, conditional density, best predictor function, Bayesian analysis, etc., connected with this new density are also introduced. Suitability of this density as a good model in Bayesian inference and regression theory is also discussed.
TL;DR: In this paper, lower and upper triangular factorizations of the complex Wishart matrix were studied and several expected values of scalar and matrix valued functions of the matrix were obtained. But these results were restricted to the complex case.
Abstract: In this article, we study lower and upper triangular factorizations of the complex Wishart matrix. Further, using these factorizations, we obtain several expected values of scalar and matrix valued functions of the complex Wishart matrix. We also generalize Muirhead's identity for the complex case which gives a number of interesting special cases.
TL;DR: In this article, the product of the inverse Wishart matrix and a normal vector is analyzed and the explicit joint distribution of the components of the product is derived, and several exact tests of general linear hypothesis about the elements of a product are presented.
Abstract: . In this article we analyse the product of the inverse Wishart matrix and a normal vector. We derive the explicit joint distribution of the components of the product. Furthermore, we suggest several exact tests of general linear hypothesis about the elements of the product. We illustrate the developed techniques on examples from discriminant analysis and from portfolio theory.